COUNTlfcw  B^>' 


THOMSON'S    NEW    MATHEMATICAL  .SFRIES. 


ILLUSTRATED 

TABLE-BOOK, 

OR 

JUVENILE  ARITHMETIC, 

CONTAINING 

ORAL    AND    SLATE    EXERCISES 

FOR 

BEGINNERS. 


BY  JAMES  B.  THOMSON,  LL.D., 

-tW   GRADED   SERIES   OK  ARITHMETICS,   PRACTICAL  ALGEBRA^SETC. 


NEW    YORK: 
CLARK  &  MAYNARD,  PUBLISHE 

5  BARCLAY  STREET, 
1880. 


THOMSON'S.-  MATHEMATICAL 'SERIES. 


I.  A  Graded  Series  of  Arithmetics,  in  three  Books,  ; 

New  Illustrated  Table  Book,  or  Juvenile  Arithmetic. 

oral  and  >.  :ses.     (For  begh. 

New  Rudiments  of  Arithmetic.     <  '..muihiu^  Mental  with  V. 
t.-n  Arithniftic.     (For  Iuterim-J,i:ite  Classes.) 

New  Practical    Arithmetic.     Adupti-d   \<>  a  romplete  business 
»-du.  •;.•  r  Qraamuur  Departments.)    Ub' 

II.   Independent  Books. 


Key  to  New  Practical  Arithmetic.    <  ..ntainiii^  ;able 

(For  teac 


New   Mental   Arithmetic.  pie  and  ('<>iu- 

il".»r  I'riitmry  Scliools.)    144pp. 

Complete  Intellectual  Arithmetic.    Specially  adapted  to  (.'looses 
:  ammar  Schools  and  Academies.     168  pp. 

III.  Supplementary  Course. 
New  Practical  Algebra.     Adapted  to  Hiirli  S.hoola  and  Acad- 

Key  to  New  Practical  Algebra.      \Vitl»  full  »•!  For 

!  pp. 

New  Collegiate  Algebra. 
Complete  Higher  Arithn.  |in-|.anu, 

' 


IfO*.  hy  JA»FJ»  II. 


PREFACE. 


IN  order  to  pursue  the  study  of  Arithmetic  with  pleasure  and 
success,  two  things  are  essential.  First,  the  elementary  princi- 
ples and  7 \ilile*  must  be  thoroughly  understood;  Second,  their 
application  mu>  perfectly  familiar. 

The  Raised  Table  Book  is  designed  to  assist  both  the  teacher 
and  the  pupil  in  the  accomplish  in ent  of  these  important  ends. 
It  is  constructed  on  the  following  plan  : 

1.  As  soon  as  a  child  learns  a  fact  or  principle  in  arithmetic, 
he  is  taught   it.s  nintH'-ilion,  and  begins  to  practice  it.     In  this 
\v.iy  an  inter  -st  is  awakened  in  the  subject,  and  the  pupil  is 

1  from  the  irks  nneness  of  learning  and  repeating  it]y- 
stract  results  and  principles,  while  i'juorant  of  their  nature  and 
use. 

2.  The  pupil  is  taught  to  iUuttrate  and/arm  the  Simple  Tables 
for  himself.     A  child   g-iins  a  much  ele.-irer  idea  of  a  thing  by 
(1  -i:iur  it  himself,  than  by  having  his  teacher  do  it  for  him. 

3.  Alternate    Mental    and    Slate    Exercises   are   inters-;' 

iiout  the  book.     These  exercises  are  carefully  adapted  to 

the  capacity  of  beginners,  and  to  the  principles  they  are  designed 

to  illustrate.      They  should  therefore  l>e  made  perfectly  familiar 

.  //  either  at  home  or  at  school.     In  this 

w.iy  the  pupil  will  learn  how  to  study,  how  to  think,  and  how  to 

4    Sp.-1-inl   pnin.«  have  been  taken  to  correct  the   Tables  of 
11',  i/hfH  «,,<l  Mi'iimirt'*,  according  to  present  Law  and  usage  ;  the 
o!>s  Y.ctr  denominations  sin-.l  those  not  used  in  the  Unitrd  Stairs 
I  carefully  excluded. 

191 


k  .  .    ,  ;    PREFACE. 

-l&ginnere  in  Arithmetic  should  be  furnished 
:•  irf  table*. '(oob ;  «fl/8laui  blackboards,   numeral    IV 

.•duntrng-  toartfe,^  etc. ,  and  bt  > 

learning  to  count,  and  in  illustrating  the  elementary  cor 
tions  and  principles  <>t  numbers. 

M»T(ibU  objfct*u*ed  for  counters,  or  unit  marks  made  ! 
pupil  uj*>n  a  slate  or  blackboard,  are  pr.-f. Table  to  the  fated 
seen  in  pictures,  or  the  stationary  numbers  r 

_rht  lines,  or  other  unit  marks  upon  charts  and 
wall  maps. 

Tli.  •  a  BOARD  is  a  new  and  valuable  acces 

api>aratii8  of  primary  schools.     Its  length  d<  M  the 

•  the  recitation  r-xn!!.  an.l  tljenunilHT  'ntheclttfc 
Wli«'ii  placed  apainst  the  wall,  its  wi.l                   :iy  fn>m  i  = 

-  ;  the  upj>er  surface  i  : narks 
<>r  >r  rij*  of  wood ;  the  edges  are  faced  with  a  plain  mou 
raised  sufficiently  to  prevent  the  counters  from  rolling  off.     If 
placed  in  tin-  middle  of  the  roov 

to  allow  pupils  to  stand  on  >r.) 

NEW  YORK,  August,  1874. 


NOT  I   . 

THE  few  changes  in  the  fore  part  of  this 

•it    it*  use   in   com ' 
ions, 
iiibcr,  1877. 


COUNTING,    i 


LESSON  I. 

i.  How  many  of  these  little  girls  an^  boys  wish  to 
learn  to  count  ?     All  that  do  may  hoW  up  a  hand. 

/ 


2.  How  many  hands  dm-.s  rach  hold 


3.  How  many  are  one  hand  and  one  hand  ? 
Two. 

4.  Hmv  many  hands  have  you  ?    How  many  feet  ? 

5.  liu\v  numy  arc  two  pencils  and  one  pencil? 
Three. 


N  T  1    V 


""  6.'  £h'o\v  1110  throo  lingers  and  count  thrin, 

7.  \\hicli  is  y«.ur  ri,Lrht  hand  ?     \\hich  your  left  ? 

8.  Ilo\\  many  thumbs  liavr  Y..U  <>n  your  ri-hi  1;.. 
How  many  on  your  left  hand  ? 

9.  How  many  on  both  ? 

10.  How  many  an-  t\\o  liners  and  one 
u.  Three  is  how  many  m<m  than  i 


LESSON     II. 

To  TEACHERS.-.*  child  learns  much  tester  by  dotng  or 
thing,  than  by  simply  nptatl*g  an  explanation  which  he  hears,  bat  does 
not  understand.  Hence,  the  pupil  at  every  exercise,  should  be  called  upon 
to  do  as  much  as  possible  with  his  own  hands.  This  is  the  only  way  to  In- 
sure rapid  progress  and  a  thorough  knowledge  of  numbers. 

1.  L-  t  tach  show  me  two  fingers.    'I  irere. 

2.  (Map  your  hand-  thnr  time-  in  • 
^.    \Y1;;;' 

4.  Three  is  how  many  more 

with  your  fingers. 

5.  ('mint  tluvr.  iM-iitin.ir  lime  with  'it  hand. 

6.  Count  from  three  back 

7.  Each  show  t! .:  Xow 
the  oth.  • 

8.  How  many  are  three  fingers  and  on< 
Pbur. 

9.  How  many  are  three  pencils  and  .-il? 

10.  (Map  your  ha: 

11.  \Vh.  after  \\\ 

12.  II  -\\  man\  BlOPe  than  three  is  ft.ur?     Than  one? 
i;v  What  e  >ur?     Hef  uv  thn 

14.  Count  from  four  >:ic. 


r  0  T  N  T  I  N  (J  .  7 

15.  How  many  lingers  on  your  left  hand?    '-Four." 

16.  Count  your  thumb  with  them;  how  many? 
Fire. 

17.  Count  five  in  concert,  beating  time. 

1 8.  Count  from  five  hack  to  one.     Twice  more. 


LESSON     III. 

1.  When  we  say  one,  two,  three,  four,  &c.,  what  is  it 
called  ? 

Counting. 

2.  Count  five  in  concert,  beating  time. 

3.  Rap  on  your  slate  with  your  pencil  five  times. 

4.  Copy  the  figures  used  to  express  the  first  five 
numbers,  as  I  make  them  upon  the  blackboard. 


i,  2,  3,  4,  5. 

one,  two,  three,  four,  five. 

5.  Five  is  how  many  more  than  four?     Show  it. 
fj.  Show  by  your  fingers    how   many  things  are 
denoted  by  the  figure  3.     By  2.     By  4.     By  5. 

I  '  & 


8 

7.  George  may  make  live  stiaiirht   marks  upon  tlio 
blackboard  :   tin-  others,  oil  their  .-!;. 

8.  Count  th«m.  pointing  to  cadi. 

9.  Make  another;  how  many  have  \ou  now? 

fffo. 

10.  Count  six  in  concert,  beating  tinni. 

1 1.  Show  me  six  fingers. 

12.  Make  six  raps  on  your  slate  with  your  pencil. 

13.  >  \  many  more  than  five?     Shov 

1 4.  Six  is  how  many  more  than  one  ? 

15.  What  co i.  before  si 

Before  four?     Before  thrc.  re  two? 

1 6.  Count  from  six  back  to  one. 


LESSON     IV. 

To  TEACH***.— The  division  into  k^»»on<»  i-  not  for  the  pnrpo««>  of  fixing 
the  daily  task  of  pupils,  bat  to  point  out  the  pr 

be  tMght  conw-cot ivelj.    It  may  be  nocewwry  to  subd 
them  into  tererml  recitation*.    Bat  however  thio  may  be.  the  cUu-n  should 
not  bo  permitted  to  POM  from  one  to  the  next,  till  the  former  la  thoroughly 
understood. 

i.  Here  is  a  pile  of  six  books;  if  I  put  aim; 

them,  how  many  will  ii 

.S      >'<'H. 

>unt  seven  in  concert,  beat  in  <r  • 

3.  Who  can  count  srv«-n  alone  promptly?     II 
may  try.     Carrie.     William.     Louise. 

4.  Let  cadi  j?how  me  ^even  fin_ 

5.  Count  from  seven 

6.  Seven  i>  h«>\\  many  more  QafB 

7.  Show  it  by  I'onnti 


co  u  NT  i  x  <;.  9 

8.  Seven  is  how  many  more  than  one  V 

9.  Make  seven  unit  marks  upon  your  slates. 

10.  How  many  are  seven  pencils  and  one  pencil? 
Eight. 

11.  Count  eight  in  concert,  beating  time. 

1  2.  Let  each  count  eight  alone.     (The  teacher  names 
individuals.) 

13.  Make  eight  raps  on  your  slute  with  your  pencil? 

14.  Eight  is  how  many  more  than  seven? 

15.  Show  it  by  count* 

16.  Eight  is  how  many  more  than  one? 

17.  Count  from  eight  back  to  one. 

18.  How  many  are  eight  counters  and  one  counter? 


19.  Count  nine  in  concert,  beating  time. 

20.  Show  me  nine  objects. 

21.  What  comes  next  before  nine?     Next  before 
eight?     Before  seven?     Before  six?     Before   live? 
Before  four  ?     Before  three  ? 

22.  Count  from  five  to  nine,  inclusive. 

23.  How  many  are  nine  cents  and  one  cent  more? 
Ten. 

24.  How  many  fingers  and  thumbs  has  each  ? 

25.  Count  ten,  beating  time? 

26.  Write  the  figures  denoting  six,  seven,  eight,  nine, 
ten. 

6,         7,         8,         9,         10. 

rix,  leven,          eight,  nine,  ten. 

27.  Show  by  marks  upon  your  slate  how  many  things 
are  denoted  by  the  figure  6.     By  the  figure  8.     By  the 
figure  7.     By  the  figure  9. 


10 


•   «>  r  N  T  : 


LESSON     V. 

i.  fount  tlio  !  a!N  on  tin-  iipj»cr  wire  of  tin-  Xni: 
Frame,  as  I  move  them  from  left  to  right.     1 1 


I 
many  will  it  make  rnmih-il  wit 

;v    It'I  ni.»vi-  two  on  the  nc\i.  h«>\v  many  • 

4.  If  tlmr  lulls  nn  t  .u  in;n: 

5.  If  four  bails  on  the  next,  h«>\\  numy  - 

6.  If  fi'.  >.;.  h..\v  many  ': 
~.    IT                     "ii  tli«-  next,  hiixv  niair 


c  o  r  x  T  i  x  G  .  11 


8.  If  seven  bulls  on  the  next,  ho\v  miuiy  '' 

9.  If  eight  balls  on  the  next,  how  many  ?  Eighteen. 

10.  If  nine  balls  on  the  next,  how  many  ?  Nineteen. 

11.  If  ten  balls  on  the  next,  how  many?  Twenty. 


LESSON     VI. 

1.  What  comes  next  after  ten  ?     "Eleven." 

2.  Eleven  is  how  many  moiv  than  ten?    "One." 

3.  How  represent  eleven  by  the  Numeral  Frame? 
J//.v.  By  moving  across  ten  balls  on  the  upper 

wire  and  one  on  the  next. 

4.  What  comes  next  after  eleven  ? 

5.  Twelve  is  how  many  more  than  eleven  ? 

6.  How  represent  twelve  by  the  Numeral  Frame  ? 
Ans.  By  the  ten  balls  on  the  upper  wire  and  two 

on  another. 

7.  What  comes  next  after  twelve  ? 

8.  Thirteen  islmw  manymore  than  twelve?  Than  ten? 

9.  How  show  that  thirteen  is  three  more  than  ten  V 
Ans.  By  the  ten  balls  on  the  upper  wire  and  three 

on  another. 

10.  The  meaning  of  the  word  thirteen? 
Ans.  Three  and  ten. 

11.  What  comes  next  after  thirteen  ? 

12.  The  meaning  of  the  word  fourteen? 
Ans.  Four  and  ten. 

13.  How  show  that  fourteen  is  four  more  than  ten? 

14.  What  comes  next  after  fourteen  ? 

15.  The  meaning  of  the  word  fifteen? 
Ann.  Five  and  ten. 


1'.'  •  n  r  x  T  i  x  <; . 

16.  How  show  that  lii'uvn  is  live  move  than  ten? 

17.  What  conies  n«-xt  after  lift.  •  n  r 

18.  The  meaning  nf  tin-  \\nnl  M.Meen? 

.   Six  and  i.-n. 

19.  How  show  that  >i\t<vn  is  six  in«>iv  than 

20.  Wh  next  a'u  •  een? 

21.  Next  aft-  a?      Afti-r  n 

22.  Count  from  ten  to  twenty,  u-atiiiLr  ; 

23.  \\\\. 

.  Two  tons. 

24.  Write  i:  ,vc.,  to  fifteen. 

«,        12,        13,        14,        15. 

eleven,        Uelw,      thirl**,      fovtcea,       fiftwa. 

25.  What  comes  next  after  13?  After  n?  After  14? 
After 

26.  Wliic-h  is  th.  ;i..\v 
show 

27.  Write  the  figures  denoting  sixt 

16,       17,        18,       19,       20. 

liiteeo,     WTfnUfn,    elghteo,     ninetwa,      tu 

28.  Which  is  the    greater,  seventeen   or 

Sli«»\v  it. 

29.  Which  is  the  greater,  nineteen  or  eighh 

30.  Write  in  liirurrs  thin 

••ixti'i-n.  fU'vi'ii.  t\\ 

^y  Haviiiir  h-arncd  to  cf)tint  ton,  childron  will  easily  l.-nrn  to 
count  from  U-n  l«er\-ing  that  after  twd\ 

names  of  the  successive  nuinlKTs  arc  formed  by  prefixing  the 
names  of  the  numlx-rs.  three,  four.  live,  six,  A;- 
to  teen  or  ten.     They  will  also  find  great  assistance 
liendiiiir  the  meuniiii:  «»f  the  terms  from  ten  t«>  a  hui.ilrcd  by 
dirertinir  attention  to  their  dcrivution. 


COUNTING.  13 

LESSON     VII. 

1.  What  does  the  word  twenty  denote  ? 
A  H*.  Twenty  denotes  two  tens. 

2.  How  is  twenty  written  ? 

Ans.  By  writing  2  in  the  second  place,  with  a 
cipher  on  the  right ;  as,  20. 

3.  Count  the  marks,  as  I  make  them  upon  the  black- 
board; how  many  ?  "Ten." 

4.  Count  on,  us  1  make  another  row.     "  Twenty." 

5.  If  I  make  another,  how  many?     "Twenty-one." 

6.  If  I  make  another,  how  many  ?     "  Twenty-two." 

7.  If  another,  how  many  ?     "Twenty-three." 

8.  If  another,  how  many?     "Twenty-four." 

9.  If  another,  how  many?     "Twenty-live." 
10.  If  another,  how  many  ?     "Twenty-six." 
n.  If  another,  how  many?     "Twenty-seven." 

12.  If  another,  how  many?     "  Twenty-eiirht..'' 

13.  If  another,  how  many?     "Twenty-nine." 

14.  If  another,  how  many  ?     "Thirty." 

15.  Twenty-one  is  how  many  more  than  twenty? 

16.  Twenty-two  is  how  many  more  than  twenty? 

17.  Twenty-live,  than  twenty?     Show  it. 

18.  Twenty-seven,  than  twenty?     Show  it. 

19.  Thirty  is  how  many  more  ihun  twenty?    Show  it. 

20.  Count  from  twenty  to  thirty  in  concert. 

21.  Write  the  ligures  denoting  twenty-one,  i  \\vnty- 
two,  &c.,  to  thirty. 

22.  What  do   the   figures  23  standing  side  by  side- 
denote?     What    25?     What  27?     What  26?     What 
29?    What  28?     What  22? 


14  <_  u  L  N  T  1   X  «r  . 

LESSON     VIM. 

i.  What  i>  i lu-  niranincr  of  the  word  thirty? 

Ails.  Thirty  denotes  ////•</•  /<•//*. 
\        2.   llo\v  is  thirty  expre- 

.   1'y  writing  3  in  the  second  place  with  a 
cipher  on  the  right ;  as,  30. 

3.  Count  from  thirty  to  forty. 

4.  Write  in  tiguivs  thirty-one,  &a,  to  f« 

5.  Count  fn>m  forty  to  fifty,  in  like  manner. 

6.  Write  in  :  i-.iin  forty  to  lifty. 

7.  Wiiat  do  the  li-  iigure834? 

-?  43?  48?  50? 

8.  Count  from  lifty  to  >i\ty.  In-iti; 

9.  Hake  tlu-  iiirurc's   ill-noting    tifty-three? 
seven  ?     Fittv-ti\«-?     Fifty-i-i- 

10.  What  do  the  tiiim-  52,  denote?  54?    56?    59? 

11.  Count  from  sixty  to  seventy,  i:, 

12.  Write  the  figures  from  sixty  to  E 

13.  Count  from  seventy  to  eigh 

14.  Make  tl 
three.     Seven  ty-ti\»». 

15.  Count  from  eighty  to  nin» 

16.  Write  the  figures  from  eighty  to  ninety. 

17.  Count  from  ninety  to  a  Innul: 

18.  Write  tli-  .roni  ninety  to  a  hundi- 

19.  Wliat  do  the  iiLTii:  «t0Y      What 
Ans.  The  figures  12,  denote  i  ten  and  .?  I 

21  denotes  j  tens  and  i  unit. 

jo.  What  do  t  lie  figures  34  denote  ?    47?    63? 
SSi"     <;;,?     ioo? 


COU.X1ING.  15 


LESSON     IX. 

To  TEACHERS.  —  Ae  i?oon  as  children  have  learned  to  count  and  write  one 
hundred  with  accuracy,  they  will  find  no  difficulty  in  counting  and  writing 
larger  numbers. 

1.  Count  from  one  hundred  to  one  hundred  and  ten. 

2.  Write  the  figures  from  one  hundred  to  one  hun- 
dred and  ten. 

100,    101,    102,    103,    104,    105,    106,    107,    io8cV£OQd 

3.  IIow  is  one  hundred  and  ten  expressed  °t 

A/i*.  Hy  writing  i   in  the  third  place,  i   in   the 
second,  and  a  cipher  in  the  first  ;  as,  no. 

4.  Count  from  one  hundred  and  ten   to  one  hun- 
dred and  twenty. 

"One  hundred  eleven,  one  hundred  twelve,  &c." 

5.  Write  in  figures  from  no  to  one  hundred  twenty. 

in,    112,    113,    114,    115,    116,    117,    118,    119,    120. 

6.  Count  from  one  hundred  twenty  to  one  hundred 
thirty,  in  like  manner. 

7.  Count  from  one  hundred  thirty  to  one  hundred 
forty,  and  so  on  to  two  hundr-'d. 

8.  Write  in  figures  one  hundred  thirty.     One  thirty- 
seven.     One  thirty-nine. 

9.  Write  in  figures  each  decade  from  140  to  200. 
10.  What  do  the  figures  135,  denote? 

.I//*.  One  hundred,  3  tens,  and  5  units. 

n.  What  do  the  figures  124,  denote?  136?  140? 
159? 

12.  What  do  the  figure-  160,  denote?  177?  185? 
188?  190?  199?  200? 


1G  C  O  U  X  T  1  N  G. 

LESSON     X. 

1.  I  low  is  two  hundred  expressed  by  figure 
Ans.  By  writing  2  in  the  third  place,  wit1 

ciphers  on  the1  ri:rht ;  as,  200. 

2.  How  cxpr.-ss  three  hundred  ?    Four  hundred,  Ac., 
t<»  nine  hundred  'i 

3.  W rile  in  figures  two  hundred  and  ten.    Two  hun- 
dred ;md  twenty.  &<•..  to  three  linndred. 

4.  Write  three  linndred  Mveniy-ihe.     Three  hn; 
iorty-.-ix.     Three  hundred  iit'iy-iniir. 

5.  Write  five  liundn-d    t\vi'iity-sc\ 
t'iirht.     Five  forty-six.     Fivesixty-i 

6.  Write  six  hundred  thirty-! 
Six  fifty-tun.     >e\en  nineM-toiir. 

7.  Write  nine  hundred  iii'teen.     Nine  twenty-* 
Nine  torty-tli roe.     Nine  sixty.     Nine  ninety-nine. 

8.  What  do  the  figures  235,  denote? 
Ann.  2  hundreds,  3  tens,  and  5  units. 

9.  What  do  the  figures  in  346,  denote  ?     In  378  ? 
<       .  and  read  the  following  numbers: 

j.  408.  10.  525.  19.  703. 

2.  310.  II.    405.  20.    890. 

3.  101.  12.    239.  tl,    875. 

4.  230.  13.    350.  22.    940. 

5-  '75-  M-  475-  23-  963- 

6.  240.  15.  509.  24.  893. 

7.  301.  16.  643. 

17.  538.  26.  990. 

9.  305.  1 8.  720.  27.  1000. 

(For  explanation  of  terms,  sec  p.  40.) 


ADDITION    TABLES. 


LESSON  I. 

To  TEACHERS. — The  present  Lesson  consists  in  adding  the  unit  one  to  the 

several  digits  in  succession.    As  the  results  correspond  with  the  regular  in- 

of  numbers  by  counting,  they  need  no  further  illustration.    The 

object  of  the  next  ei<,'ht  k-«sons  is  to  fiamiliartee  the  learner  with  the  addition 

of  the  other  digits  to  each  other. 


0  and  I  are  I.  5  and 

1  "  I         "  2.  6  " 

2  «  I         «  3.  7  " 

3  -  i      «  4.  8  « 


are  6. 

"  7- 

"  8. 

"  9- 

«  10. 


4  l  5-  9 

1.  If  you  have  three  pears  and  I  give  you  one  pe;ir, 
how  many  pears  will  you  have  r* 

SOLUTION. — Three  pears  and  i  pear  are  4  pears. 

2.  How  many  are  4  apples  and  i  apple  ?     Show  it 
with  your  fingers. 

3.  How  many  are  5  pencils  and  i  pencil  ?    Show  it. 

4.  George  had  6  cents  and  earned  i  more :  how  numy 
had  he  then  ? 

5.  How  many  are  7  marbles  and  i  marble?     Show  it. 

6.  Eight  tops  and  i  top  are  how  many  ?     Show  it. 

7.  If  a  teacher  has  9  roses  and  a  pupil  gives  her  i 
more,  how  many  roses  will  she  have  ? 

8.  Write  the  following  numbers  in  figures :  Thirteen, 
eleven,  nineteen,  twenty,  twenty-five,  thirty,  and  forty. 

2 


0 

and 

2 

are 

2. 

5 

I 

*< 

2 

u 

6 

2 

.. 

2 

4- 

7 

3 

M 

2 

5- 

8 

1  •-  ADDITION. 

LESSON     II. 

To  TKAcmcB*.-Tbe  Addition  Table  of)  may  be  illustrated  thoa: 

:j:  ind   :•:    :*:  an-  /; 
:£   #  and  :*:    :•: 

"i*        •'•        •*•       .|lul       *4?        *if 

»y»          •*•  »^»        tlllVA         (r^»          *•* 

'•••    .*:'•    :•'-    :•:  and  ^    *    *k   *«,  &c. 

Let  the  elans  nniah  the  illwtration,  writing  the  table  out  in  full. 

and       2      are      J. 

10. 

4      "       2      "      6.  9      "       2      "    ii. 

1.  If  ("Jrori;.-   ha-   4    ]>mcils  and   l»n\-   2   more,  hoW 
many  pencils  will  he  h; 

- 

2.  How  many  are  3  slates  and  2  slates  : 

.;.   How  many  are  5  hats  and  2  hats?     Sliou 

4.  How  many  are  6  roses  and  2  roses? 

£   How  many  an-  S  cherries  and  2  chcr 

6.  Add  2  to  itself  continually,  till  the  sum  is  50. 

•y  and  add  the  following : 
(7.)         (8.)        (9.)       (10.)        u.)      (12.)      (. 

I  I  I  2  2  I  2  I 

2221  I  2  I 

3465728 


r  — As  Mwn  a*  the  combination*  of  the  digite  are  andcrMood.  they 
fhould  be  PO  thoroughly  flxM  in  the  memory,  that  when  any  result  is  re- 
quired, it  should  instantly  flash  upon  the  mind. 


A  D  D  1  T  I  0  X  .  19 

LESSON     III. 

0  and       3      are      3.  5      and      3      are      8. 

1  "  3  "  4-  6  «  3  "  9. 

2  «  3  "  5-  7  "  3  "  I0- 

3  «  3  "  6.  8  "  3  "  ii. 

4  "  3  "  7-  9  "  3  "  12. 

1.  How  many  are  4  boys  and  3  boys?     Show  it. 

2.  How  many  are  5  needles  and  3  needles  ?     Show  it. 

3.  George  has  3  flowers  in  one  hand  and  6  in  the 
other:  how  many  has  he  in  both  hands? 

4.  3  cents  and  9  cents  are  how  many  cents? 

5.  7  knives  and  3  knives  are  how  many  ? 

6.  If  8  chickens  are  under  the  coop  and  3  outside  of 
it.  how  many  chickens  are  there  in  all  ? 

7.  Harry's  kite  line  is  9  yards  long:   if  he  ties  on 
3  yards  more,  how  long  will  it  then  be? 

8.  Add  3  to  itself  continually,  till  the  sum  is  60. 

9.  What  is  uniting  two  or  more  numbers  in  one, 
called  ? 

Addition* 

10.  What  is  the  result  or  number  obtained  called? 
The  Suui  or  Amount. 

11.  When  we  say  2  and  i  are  3  and  2  are  5,  which 
is  the  sum  ? 

Copy  and  add  the  following : 
(12.)      (13.)     (14.)     (15.)     (16.)     (17.)     (18.)     (19-) 

2  I  232223 

3  3  3          3          3          3  '  i 
45            346789 


A  I)  I)  1  T  10  N. 

LESSON     IV. 


0 

..M.l 

4 

•re 

4- 

5 

and 

4 

«rr 

9- 

I 

.. 

4 

.. 

5- 

6 

U 

4 

.. 

10. 

2 

ft 

4 

« 

6. 

7 

.. 

4 

* 

i  i. 

3 

flf 

4 

H 

7- 

8 

4 

4 

ft 

4 

M 

s. 

9 

.. 

4 

t( 

i    II  v,  many  are  4  grapes  and  5  grapes? 

2.  Charles  has  4  credits:  bow  many  U\UA  \ 
have  7  ? 

3.  4  and  what  number  are  6? 

1  f  you  lia  <  I  tits  and  buy  4  more,  how  many 

will  you  thru  huve? 

5.  How  many  arc  9  cents  and  4  cents? 

6.  7  ducks  and  4  ducks  are  how  many  ? 

7.  Uilliain  has  4  apples  and  (Jeorge  has  4  11: 
William:  how  many  has  Geor^: 

8.  How  many  are  8  girls  and  4  gir 

9.  Julia  has  4  peaches  and   1  -iv  than 
.Tnlia  :  how  many  has  Fain 

10.  How  many  are  9  tops  and  4  tops? 

1 1.  Add  4  to  i!>i'lf  continually  till  the  sum  is  60. 

Copy  and  add  the  following: 
(12.)      (13.)     (14.)      (15.)      (16.)     (17.)     (i 

I    2234323 
21432144 

3     4     3     2     l     4     i 
43242342 
54          6          7          Q 


A  1)  D  I  T  I  O  X  .  '.'  I 

LESSON     V. 

0  and       5      are      5'  5      au(l      5      ar*      1O' 

1  "  5  "  6.  6  "  5  "  ii. 

2  "  5  "  7-  7  "  5  "  12. 

3  "  5  "  8.  8  "  5  "  13. 

4  «  5  «  9.  9  «  5  «  14. 

1.  5  pencils  and  3  pencils  are  how  many? 

2.  5  apples  and  4  apples  are  how  many  ? 

3.  There  are  5  birds  on  one  tree  and  5  on  another : 
how  many  birds  are  on  both  trees? 

4.  On  one  rose-bush  are  6  buds,  and  on  another  5 : 
how  many  buds  are  on  both  ? 

5.  How  many  are  5  trunks  and  7  trunks? 

6.  How  many  are  S  guns  and  5  guns? 

7.  Moses  wrote  9  lines  and  Margaret  5  lines:  how 
many  lines  did  both  write? 

8.  Add  5  to  itself  continually,  till  the  sum  is  60. 

9.  How  many  are  ii  and  5?     12  and  5?     14  and 
5?     13  and  5?     16  and  5?     15  and  5?     iSands? 
17  and  5  ?     19  and  5? 

10.  Write  the  following  in  figures:  Forty-nine,  Fifty- 
two,  Sixty-seven,  Eighty-one,  Seventy-four,  Eighty-six, 
One  hundred  and  fifteen. 

Copy  and  add  the  following : 
(n.)   "(12.)     (13.)      (14.)     (15.)     (16.)     (17.)    (18.) 


2 

2 

4 

2 

4 

4 

2 

4 

3 

I 

2 

3 

3 

i 

4 

2 

2 

3 

3 

5 

i 

2 

5 

3 

5 

5 

5 

4 

2 

5 

3 

5 

£ 

4^ 

A 

2 

5 

3_ 

4 

2 
i-.- 

A    D  D  1 1    1  «  '   N  . 


LESSON     VI. 

0  and      6      are  5      and      6      are   1  I. 

1  "  o  "  7.  6"6      -    12, 

2  "  6  "  8.  7      "       6      •• 

3  "  6  8      "       6 

4  «  6  "  10.  9      "       6 

1.  H.'W  many  are  5  dollars  and  6  dolla: 

2.  If  yon  have  6  pears  and  buy  4  more,  how  many 
will  you  thru  ha\ 

j,   11   u  many  are  10  melons  and  6  mel 

4.  It'  you  pick  6  peaches  from  ODI  ind  7  from 

now  many  \\\\\  yoi, 

5.  If  there  are  8  birds  on  a  tree,  and  6  mo: 
.1,  how  many  arc  there  in  all  !' 

6.  George  paid  6  cents  for  a  ball,  and  6  cents  f 
orange  :  how  many  cents  did  he  pay  for  both  ? 

7.  Add  6  to  itself  cjnitinually,  till  i  Ifl  60. 

8.  Express  Forty-four  in  figareh, 

.  Eighty-t 

9.  How  mai  13  and  6?     1431 

12  and  6?     15  and  6?     17  and  6?     i6and6?     18 
and  6?     19  and  6? 

•:d  add  the  following: 

(10.)    (II.)     (12.)      (I3.)      (I4-)      (I5-)     (16.)       (I?-)     (13.) 

5 

4  2 

5  3 

6  6 

3          4 


4 

3 

2 

4 

2 

5 

3 

5 

4 

3 

4 

4 

5 

2 

6 

3 

6 

3 

6 

4 

6 

4 

6 

5 

6 

3 

6 

5 

2 

4 

3 

2 

4 

5 

ADDITION. 

LESSON     VII. 

0  and       7      are      7.  5      and       7      are   12. 

1  "  7  "  8.  6  "  7  "    13. 

2  "  7  "  9.  7  "  7  "    14- 

3  «  7  «  10.  8  «  7  "15. 

4  "  7  "  n.  9  "  7  "    16. 

1.  Sarah  has  3  dolls,  and  Louise  has  7  :  how  many 
have  both  ? 

2.  5  hats  and  7  hats  are  how  many  ?     6  and  7  ? 

3.  George  spent  4  cents  for  marbles,  and  7  cents  for 
a  sponge  :  how  many  cents  did  he  spend  in  all  ? 

4.  How  many  are  7  dollars  and  5  dollars  ?     8  and  7  ? 

5.  Charles  obtained  12  credits  in  the  morning,  and 
7  in  the  afternoon :  how  many  had  he  in  both  ? 

6.  How  many  are  7  caps  and  9  caps  ? 

7.  George  has  8  doves,  and  has  sold  7 :  how  many 
had  he  at  first  ? 

8.  Add  7  to  itself  till  the  sum  is  70. 

9.  Express    in    figures,  Fifty-nine,    Seventy-eight, 
Eighty-four,   Sixty-two,   Ninety-three,   Ninety-seven. 

10.  How  many  are  n  and  7  ?     12  and  7  ?     14  and 
7  ?     13  and  7  ?     15  and  7  ?     18  and  7  ?     19  and  7  ? 

Copy  and  add  the  following : 


(II.) 

(12.) 

(13.) 

(14.) 

(IS-) 

(16.) 

(170 

(18.) 

4 

2 

3 

5 

4 

5 

6 

4 

2 

3 

5 

4 

5 

3 

5 

2 

3 

7 

3 

3 

2 

6 

4 

3 

7 

6 

4 

2 

3 

7 

5 

7 

6 

5 

7 

6 

7 

2 

6 

2 

3 

4 

_3 

4 

_5 

_4 

J 

,'l  A    Ii  I)  I  T  I  ..   N "  . 

LESSON     V  I  I  I, 

0  and      8      are      8.  5      and      8      AM   13. 

1  ••       8      "      9.  6      "       8      "    14. 

2  u      8      "    Jo.  7      "       8      "    15. 
'  3      «       8      "    ii.                   8      "       8      "    16. 

4      "       8      «    u.  9      "       8      "    17. 

1.  .Tune  hud  2  needles  on  IKT  \v»»rk.  and  8  ii; 
needlcbook  :  how  many  had  she  in  all  'i 

2.  Julia  paid  8  cents  for  a  thimMr.  and  5 

a  spool  of  cotton :  h<»\v  much  did  .-In-  p.:  M  ? 

3.  How  many  are  7  yards  and  8  y;  and  8  ? 

4.  Edward  bought  figs  for  6  cents,  and  cakes  for  8 
- :  how  much  did  he  pay  for  Imih  ? 

manyaiv  4  IV-et  and  8  : 

6.  One  pupil  gave  the  teacher  7  pinks,  and  an<>th«  r 
gave  8 :  how  many  did  hot 

Id  8  to  itself  t  un  is  80. 

8.  Write  in  figures,  1 

ighty-eigi  y-six,  a  IIiuu, 

9.  How  many  are  1 1  and  8  ?    13  and  8  r     i2;md8? 
14  and  8?     16  and  8?     15  and   8?     17  and  S  ?     19 

8? 

Copy  and  add  the  following : 

(10.)  \n.)  (12.)   (13.)   (14.)   (15.)  (16.)  (17.) 
6s624566 
54233375 
3^355          47 
438          2566 

8845          7 

A   ±    5    1.   -   A       7 


ADDITION.  °:> 

LESSON     IX, 

0  and      9      are      9.  5      ami      9      are   14. 

1  «  9  «  10.  6  "  9  "  15. 

2  "  9  "  ii.  7  "  9  "  16. 

3  "  9  "  12.  8  "  9  "  17. 

4  "  9  "  13.  9  "  9  "  1 8. 

NOTE. — The  first  five  numbers  are  easily  added.  The  re- 
sults of  adding  9,  being  i  less  than  if  10  were  added,  are  also 
easily  remembered.  The  ethers,  6,  7,  8,  are  more  difficult,  and 
therefore  should  receive  *pc<'i<il  <  it  tendon. 

1.  Charlotte  solved  4  examples  in  Addition,  and  9 
in  Subtraction :  how  many  did  she  solve  in  all  ? 

2.  James  has  3  pears,  and  gave  away  9  :  how  many 
had  he  at  first  ? 

3.  How  many  are  6  books  and  9  books  ?    9  and  7  ? 

4.  9  dollars  and  5  dollars  are  how  many  dollars  ? 

5.  Joseph  played  5  games  of  checkers,  and  9  games 
of  dominoes :  how  many  games  did  he  play  in  all  ? 

6.  William  is  8  years  old  :  how  old  will  he  be  9  year* 
hence  ? 

7.  Helen  has  given  away  9  apples,  and  has  6  left  : 
how  many  had  she  at  first  ? 

8.  Add  9  to  itself,  till  the  sum  is  90. 
Copy  and  add  the  following : 


(9-) 

(10.) 

(n.) 

(12.) 

(T3-) 

(140 

(I5-) 

(16. 

8 

5 

8 

5 

6 

8 

7 

9 

7 

9 

5 

6 

5 

7 

8 

6 

7 

5 

4 

7 

7 

5 

7 

8 

5 

8 

6 

9 

3 

9 

6 

7 

9 

7 

9 

4 

9 

7 

8 

9 

4 

6 

3 

7 

8 

6 

7 

<S 

•;i;  A  Dli  IT  IK 

LESSON     X. 

Oral    l)i  ill. 

To  TEACHERS.—  The  object  of  this  and  other  Oral  Drill*,  i»  to 
accurate  and  rapid  combinations.     Each  example  should  be  continued 
through  the  ti-n  decades,  and  be  dwelt  upon  till  perfectly  familiar. 

1.  How  many  arc  2  and  10?  12  and  10  ?  22  ami 
10  ?  32  and  10  ?  42  and  lo  ?  etc.,  to  92. 

2.  2  and  2  ?  12  and  2  ?  22  and  2  ?  etc.,  to  92. 
.V  i  and  3  't  ii  and  3  !r  21  and  3,  etc.,  to 

4.  2  and  3  'i  12  and  3  ''  22  and  3,  etc.,  to  < 

5.  3  and  3  ?  13  and            ;,  etc.,  to  96  ? 

6.  i  and  4  ?  1  1  and  4  ?  21  and  4  ?  31  and  4  ? 

7.  2  and  4  ?  12  and  4  ?  22  and  4  ?  32  and 

8.  3  and  4  ?  13  and  4  ?  23  and  4  ?  33  . 

9.  4  and  4  ?  14  and  4  ?  24  and  4  !"  34  and  4  ? 
10.  3  and  10  ?  13  and  10  ?  23  and  10  ?  etc, 

1  1.  4  and  10  ?  14  and  10  ?  24  and  10  ?  etc. 

12.  5  and  10  ?  15  and  10  ?  25  and  10  ?  . 

13.  f»  and  10  ?  16  and  10  ?  26  and  10  ?  • 

14.  7  and  10  ?  17  and  10  ?  27  and  10  ?  etc. 

15.  8  and  10  ?  18  and  10  ?  28  and  10  ?  etc. 

16.  2  and  5  ?  12  and  5  ?  22  and  5  ?  32  and  5  '.' 

1  7.  3  and  5  ?  13  and  5  ?  23  and  5  ?  33  and  5  ?  etc. 
18.4  and  5?  14  and  5  ?  24  and  5  ?  34  and  5  ?  etc. 
19.  5  and  5  ?  15  and  5  ?  25  and  5  ?  35  and  5  ?  etc. 


The  Irnrwr  will  observe  that  the  right  hand  figure  <>f 
flu-  sinn  *>f  tw»  dibits  in  <  \.  ry  decade,  is  always  the  same. 
Thu*.  3  and  4  are  7  ;  13  and  4  are  17  ;  23  and  4  are  27,  etc.,  the 
ri^rht  hand  figure  being  ahv 


A  D  1)  1  T  I  O  N  .  Zi 

LESSON     XI. 

1.  How  many  are  2  and  6  ?    12  and  6  ?    22  and  6  ? 
32  and  6?     42  and  6V     52  and  6?     62  and  6?     72 
and  6?     82  and  6  ?     92  and  6  ? 

2.  3  and  6  ?    13  and  6  ?   23  and  6  ?   33  and  6  ?  etc. 

3.  4  and  6  ?    14  and  6  ?    24  and  6  ?   34  and  6  ?  etc. 

4.  5  and  6  ?    15  and  6  ?   25  and  6  ?   35  and  6  ?  etc. 

5.  6  and  6  ?    16  and  6  ?   26  and  6  ?  36  and  6  ?'etc. 

6.  i  and  5  ?    n  and  7  ?    21  and  7  ?   31  and  7  ?  etc. 

7.  2  and  7  ?    12  and  7  ?   22  and  7  ?   32  and  7  ?  etc. 

8.  3  and  7  ?    13  and  7  ?   23  and  7  ?   33  and  7  ?  etc. 

9.  4  and  7  ?    14  and  7  ?    24  and  7  ?   34  and  7  ?  etc. 

10.  5  and  7  ?    15  and  7  ?   25  and  7  ?   35  and  7  V  i-lc. 

1 1.  6  and  7  ?    16  and  7  ?    26  and  7  ?   36  and  7  ?  etc. 

12.  7  and  7  ?    17  and  7  ?    27  and  7  ?   47  and  7  ?  etc. 

13.  nandS?   21  and  8?   31  and  8?   41  and  8  ?  etc. 

14.  2  and  8  ?    12  and  8  ?   22  and  8  ?   32  and  8  ?  etc. 

15.  3  and  8  ?    13  and  8  ?   23  and  8  ?   33  and  8  ?  etc. 

1 6.  4  and  8  ?    14  and  8  ?    24  and  8  ?   34  and  8  ?  etc. 

17.  5  and  8  ?    15  and  8  ?    25  and  8  ?   35  and  8?  etc. 

18.  6  and  8  ?    16  and  8  ?    26  and  8  ?   36  and  8  ?  etc. 

19.  7  and  8?    17  and  8?   27  and  8  ?   37  and  8?  etc. 

20.  8  and  8  ?    18  and  8  ?   28  and  8  ?   38  and  8  ?  etc. 
Write  the  following  numbers  in  figures :  » 

21.  Fifty-seven,    Sixty-eight,  Eighty,  Ninety-three, 
One  hundred  and  one,  One  hundred  and  ten. 

Copy  and  read  the  following : 

22.  no  25.     139  28.  205  31.  480 

23.  125  26.    203  29.  250  32.  308 

24.  108  27.    230  30.  319  33.  500 


A  1)  1.  1  T  I  o  N  . 


LESSON      XII. 

1.  How  many  arc  i  and  9?     n  and  9  .-  19? 
31  and  9?    41  and  9?    51  and  9?    61  and  9?     71 
and  9  ?    81  and  9  ?    91  and  9  ? 

2.  2  and  9?     12  and  9?     22  and  9?    32  anc 
42  and  9  ?    52  and  9  ?    62  and  9  ?     72  and 

3.  3  and  9  ?     13  and  9  ?    23  and  9  ?    33  and  9 ': 
and  9?  etc. 

4.  4  and  9  ?    14  and  9  ?    24  and  9  ?  34  and  9?  etc. 

5.  5  and  9?    15  and  9?     25  and  9?    35  and  9?  etc. 

6.  6  and  9?     16  and  9  ?     26  and  9  ?    36  and 

7.  7  and  9  ?     17  and  9?     27  I 

8.  8  and  9  ?    18  and  9  ?    28  and  9  ?   3  - 

9.  9  and  9  ?    19  and  9  ?    29  and  9  ?    3 

10.  Count  by  twtt  till  you  reach  60. 
four,  six,  eight,  ten,  t\\ 

1 1.  Count  by  33  till  you  reach  60. 

12.  Count  l>y  43  till  you  reach  60. 

13.  Count  by  53  till  you  reach  60. 

14.  Count  by  6s  till  you  reach  60. 

15.  Count  by  73  till  you  reach  70. 

1 6.  Count  by  8s  till  you  reach  80. 

17.  Count  by  95  till  you  reach  90. 

1 8.  Count  by  los  till  you  reach  100. 

Copy  and  read  the  following : 

19.  506         22.     883         25.     1,007         28.    32,368 

20.  610         23.    915          26.     2,100         29. 

21.  740          24.     999          27.     3,075          30.  568,073 
r  <^xplauation  of  terms  iu  Addition,  see  p.  48.) 


SUBTRACTION    TABLES. 


LESSON      I. 

To  TEACHERS.— The  object  of  this  Lesson  i*  to  familiarize  the  learner 
with  the  natural  decrease  of  \hc  first  ten  numbers. 


from     I    leaves    O. 

I     from    6    leaves    5* 

"        2          «          I. 

i      "      7       "       6. 

"      3       "       2. 

i      «      8       "       7. 

"      4       "       3- 

i      "      9       '•       8. 

"     5       "      4- 

I         "      10          "          9. 

1.  Here  arc  4  books:   if  I  take  i  away,  how  many 
will  be  left  ? 

SOLUTION. — i  book  from  4  books  leaves  3  books. 

2.  If  George  has  3  apples,  and  gives  i  to  his  sister, 
how  many  will  he  have  left  ? 

3.  If  Henry  has  5  cents,  and  pays  i  cent  for  a  pen- 
cil, how  many  cents  will  he  have  left  ? 

4.  James  being  asked  how  many  marbles  he  had, 
'vplied  he  had  6,  lacking  i :  how  many  had  he  ? 

5.  If  you  have  8  pears,  and  eat  i,  how  many  will 
you  have  left  ? 

6.  One  pen  from  9  pens,  leaves  how  many  ? 

7.  James  caught  *0  butterflies,  and  i  of  them  IUi\v 
away  :  how  many  did  he  have  left  ? 

8.  i  from  10  leaves  how  many  ?     i  from  9  ?     i  from 
6  ?     i  from  5  ?     i  from  4  ?     i  from  3  ? 


30  9  I    IITK  ACT  [OH. 


LESSON      II. 

To  TEACHKRS.—  The  class  can  readily  iUn-innr  ih-    Snbtrnr  ti<m  Table  of 
2,  in  the  following  main 

Make  2  marks       (i  i)  ;  cancel  2,  none  arc-  Vk 

"     3     "         (in);  cancel  2,  one  is  l<Tf.  1%  i. 

"     4     "        (i  in);  cancel  2,  two  are  left,      1! 
"     5     "      (inn);  cancel  2,  three  are  l«it.  H.  ii  i. 

Let  the  class  continue  the  illustration,  and  write  oat  the  Table,  as  below. 

from       7     leave*    5. 

"        8       "       6. 


2     from    2     l«  at  »• 

•    0. 

4 

2 

2        "        3          " 

•M 

2 

t      "      4       " 

z- 

2 

-      "      5       " 

iv 

2 

2        "        6          « 

4- 

2 

10       " 

11- 

i.   William   had  I,  and  pave  2  t«»  his  hi 

many  did  he  then  hu\ 
SOUJTION.—  2  oranges  from  5  oranges  leave  3  oranges. 

If  you  pay  3  cents  I'm-  -\  sponge,  and  sell  i1 
2  cents,  how  m  n  c!i  will  you  lose? 

3.  Two  and  what  number  aiv  7  ?     2  from  7  ? 

4.  Eight  less  2  are  how  many  ?     2  and 

5.  What  nnmher  is  2  less  than  10?  2  more  than  10? 

6.  Nine  peaches  less  2  peaches  are  how  many  ? 

7.  Two  and  what  numhrr  make  1  1  'J. 

8.  "What  is  taking  one  number  from  another  culled  ? 
Suhtrttction. 

9.  What  is  the  result,  or  nuniher  obtained,  called  ? 

T/tf   l>tff<'reif<-<'  />/•   Ift'iHfiiiiflci: 

10.  When  we  say  2  from  5  leaves  3,  which  is  the  re- 
mainder? 


>  I'  BIB  ACTION.  31 

LESSON     III. 

3    from    3    leave*   O.  3    from      8    leaves   5* 

3      "      4       "       i.  3  "  9  u  6. 

3      "      5       "       *•  3  «  10  «  7. 

3      "      6       "       3.  3  «  ii  «  8. 

3*7*4-  3  "  12  «  9. 

1.  John  started  with  5  pencils,  but  on  his  way  to 
school  lost  2  of  them  :  how  many  did  he  then  have  ? 

2.  If  you  have  6  cents,  and  spend  3  cents,  how  many 
cents  will  you  have  left  ?     3  plus  6  ? 

3.  How  many  are  8  less  3  ?     8  plus  3  ? 

4.  Show  each  with  your  fingers. 

5.  How  many  more  than  3  is  5  ? 

6.  Show  each  with  your  fingers. 

7.  If  you  obtain  3  credits  in  the  morning,  how  many 
must  you  get  in  the  afternoon  to  make  10? 

8.  Surah  lias  9  dollars,  and  her  sister  has  only  3  : 
how  many  more  has  one  than  the  other  ? 

9.  Susan  having  9  cents,  gave  3  of  them  to  a  pool- 
child:  ho\v  many  cents  did  she  have  then  ? 

10.  Twelve  marbles  less  3  marbles  are  how  many  ? 

11.  Write  in  figures,  One  hundred  and  five,  One 
hundred  and  ten,  One  hundred  and  thirty,  One  hun- 
dred and  forty-one. 

Copy  and  subtract  the  following : 

(12.)    (13.)   (MO   (-SO   (us.)    (•?.)    (i&)    (19.) 

12          13         14         13         16          17          18         19 
33333333 


9VB  T  K  A  <     11' 

LESSON     IV. 


-1 

from 

4 

travel 

0. 

4 

from 

9    Irnvei 

•  5- 

4 

tt 

5 

.. 

I. 

4 

.. 

10 

6. 

4 

tt 

6 

tt 

2. 

4 

U 

II 

;. 

4 

(( 

7 

tt 

3- 

4 

.. 

12 

K 

4 

tt 

8 

M 

4- 

4 

tt 

13 

9- 

1.  If  you  have  7  plums,  and  give  away  4  of  tl 
how  many  will  remain  ?    Show  it 

2.  If  4  pinks  are  taken  from  6  pinks,  how  many  will 
remain  ?     Show  it. 

3.  If  Henry  has  8  pin-wheels,  and  sells  4,  how  many 
will  he  then  have  ?    Show  it 

4.  There  are  10  balls  on  a  wire  of  the  nunu-nil  t'i 
if  I  move  across  4,  how  many  will  remain  ? 

5.  If  there  are  12  pupils  in  a  class,  and  all  are  pci 
I. ut  4,  how  many  arc  pi-rU-ct? 

6.  Charles  had  9  chickens,  but  a  hawk  killed  4  : 
many  has  he  1 

7.  How  many  are  7  pens  less  4  pens? 

8.  How  many  are  10  boys  less  4  bo 

9.  Amelia  is  13  years  old,  and  IK  is  4  years 
younger:  how  old  is  her  sister? 

10.  Copy  and  read  the  following:  147, 175,  183,  196, 
101,  105,  210,  213,  248,  260. 

Copy  and  subtract  the  following: 
(11.)     (12.)      (13.)      (14.)     (15.)     (16.)     (17.)     (18.) 
12          13          14         15          16         17         18         19 
44444444 


SUBTRACTION. 


33 


LESSO  N     V, 


fro  i 


5  Irnvc*  O. 

6  «  i. 

7  "  2. 

8  "  3- 

9  "  4- 


5    from    IO  lea-re*  5. 

"n       "  6. 

"         12  "  7. 

"      13       "  8. 

(( 


13 
M 


1.  Homer  had  8  rabbits,  and  has  sold  5  :  how  many 
has  he  now  remaining  ? 

2.  If  you  have  5  pins,  how  many  more  will  make  10  ? 

3.  Five  and  what  number  make   7?     Show  it 

4.  Ten  less  5  are  how  many  ?     10  plus  5  ? 

5.  George  caught  n  fish,  which  was  5  more  than 
his  brother  caught:  how  many  did  his  brother  catch? 

6.  How  many  are  1 1  less  5  ?     12  less  5  ? 

7.  What  number  taken  from  9  leaves  5  ? 

8.  How  many  are  13  chestnuts  less  5  chestnuts  ? 

9.  The  price  of  a  slate  is  12  cents,  and  an  inkstand 
5  cents :  what  is  the  difference  in  their  prices  ? 

10.  If  you  take  5  pears  from  a  basket  of  13  pears, 
how  many  will  remain  ? 

11.  On  a  tree  there  were  n  pigeons,  and  a  hunter 
shot  5  of  them :  how  many  were  left  ? 

12.  Express  in  figures,  Two  hundred  forty-five,  Two 
hundred  sixty,  One  hundred  eighty-three. 

Copy  and  subtract  the  following : 

(,3.)     (14.)      (15-)      ('6.)      (i?-)     (18.)     (19.)     (^o.) 
12          13          14          15  16         17          18         19 

55555555 


34  -^  f  U  T  H  A  i    T  I  o  N  . 

LESSON     VI. 

6    from       6    leaves    O.  <•     from     1  I     leaves    5. 

6  "  7  ••  i.  6  "  ;_•        -       6. 

6  «  S  ••  _.  6  "  13 

6  "  ij  6  "  14 

0  *•  10  "  4.  "  15 

1.  A  party  of  12  1  ova  were  skating,  and  6 
i>roke  through  the  ice:  how  many  c&capi 

2.  A  waiter  dropped  a  pile  of  9  plau-s,  and  ! 
but  6 :  how  many  did  he  bruik  ? 

3.  If  you  pay  8  cents  for  a  slate  and  sell  it  for  6 
B,  how  much  will  you  lose?    6  and  2  ? 

4.  IIow  many  are  10  quarts  less  6  quar 

5.  Nine   bananas  less  6   bananas  an-  how  many? 

6.  Eleven  birds  less  6  birds  are  how  ma: 

;.  The  price  of  a  hat   is  6  dollars,  and  t    u 

dollars:  what  is  the  difference  in  their  prif 

8.  Helen  is  13  years  old,  and  is  6  yearg  o; 
her  brothor :  how  old  is  her  brother  ? 

9.  A  certain  class  contained  15  pupils,  6  - 
were  girls :  how  many  boys  were  th« 

10.  George  is  now  15  years  old:  how  old  was  he  6 
ago  ?     9  and  6  are  how  many  ? 

1 1.  Copy  and  n-ad  :  175,  290,  105,  210,  245,  209. 
Copy  and  subtract  the  following : 

12.)      (13.)     (14.)      (I5-)      (16.)      (17.)     (18.)     (19.) 

12          13         14         15          16         17  19 

66  66666 


7    from       7    leaves    O. 

7    from    12 

7      ••        8       "       i. 

7      "      13 

7      «        9       «       2. 

7      "      14 

7      "      10       "       3- 

7      "      15 

7      «      ii       "       4. 

7      "      16 

SUBTRACTION.  35 

LESSON     VII. 

leaves    5* 

"       6. 

"       7- 

«       8. 

"       9- 

1.  Edward  bought  a  slate  for  10  cents,  and  paiu  7 
cents  down  :  how  much  does  he  owe  for  it? 

2.  A  lad  having  12  eggs  took  them  to  marker,  and 
on  his  way  broke  all  but  7  :   how  many  did  he  break  '{ 

3.  How  many  are  n  less  7  ?     12  plus  7  ? 

4.  If  from  a  dish  of  13  oranges,  7  are  taken  out,  how 
many  will  remain  ?     7  and  6  are  how  many  ? 

5.  Six  from   n  leaves  how  many  ?     6  from  13  ?     7 
from  13?     7  from  i  o  ?     7  from  1 1  V 

6.  Charles  had  15  young  doves,  and  a  cat  killed  7  of 
them:  how  many  did  he  then  have  ?     7  plus  8? 

7.  During  the  last  14  school  days  Julia  has  been 
tardy  7  days:  how  many  days  has  she  been  punctual  ? 

8.  Twelve  is  how  many  more  than  7  ?     What  num- 
ber must  be  added  to  7  to  make  12  ? 

9.  If  you  have   16  cents  and  spend  7  of  them  for  a 
lunch,  how  many  will  remain? 

ic.  Seven  tops  from  16  tops  leave  how  many  ? 
IT.  K\|>ivs»  in  figures.  Five  hundred,  One  thousand 
six  hundred,  Four  hundred  thousand. 
Copy  and  subtract  the  following: 

(12.)     (13.)      (14.)     (15.)     (16.)     (17.)      (i  8.)      (19.) 

13          12          16         14         15          18  19  17 

777777  7  7 


36  SUBTRACTION. 

LESSON     VIM. 

8    from       8    leaves    O.  8    from     IJ    Imvrs    5. 

8  "  9  u  i.  8  "  14  "  6. 

8  "  10  "  2.  8  "  15  «  7. 

8  "  ii  "  3.  8  "  16 

8  "  12  «  4.  8  "  17  "  9. 

1.  James  picked  13  quarts  of  chestnuts,  and  John  8 
quarts:   how  many  mmv  did  one  pick  than  the  other? 
How  many  quarts  did  k  ? 

2.  A  father  Lrave  each  of  his  two  sons  a  garden  s; 
Ider  sold  his  vegetahles  for  12  dollars,  the 

sold  his  for  8  dollars:  what  was  the  dill 
sums  eacli  received  ? 

3.  If  the  older  of  two  sisters  is  16  years,  and 
younger  8  years,  what  is  the  difference  in  their  ages? 

4.  Fourteen  peaches  less  3  peaches  are  how  mat 

5.  Eight  from  13  l»-av.-s  how  nnnv  ?     s  pin 

6.  A  market  woman  bought  15  turkeys  and  sold  8 
of  thorn  :  how  many  had  she  on  hah 

7.  If  you  walk  8  miles  in  the  morning,  how  far  must 
you  walk  in  the  afternoon  to  make  15  miles? 

8.  Eight  from  14,  how  many?    6  from  14  ? 

9.  George  saved  8  yards  of  his  kite  line,  which  was 
1 7  yards  long :  how  many  yards  did  he  lose  ? 

10.  Copy  and  read  the  following:    1510,  2620,  3 
6659,  1870,  10,807,  25,977*  85,999,  100,000. 

Copy  and  subtract  the  fallowing: 
(n.)     (12.)      (13.)      (14.)      (15.)     (16.)      (17.) 
12         13         15          16         14          17 
88888888 


SUBTRACTION.  37 

LESSON         IX. 


9 

from 

9 

leaves 

0. 

9 

from 

14 

leaves 

5- 

9 

a 

10 

a 

I. 

9 

a 

15 

(( 

6. 

9 

a 

ii 

a 

2. 

9 

ft 

16 

tt 

7- 

9 

a 

12 

a 

3- 

9 

H 

i7 

(t 

8. 

9 

a 

13 

M 

4- 

9 

(( 

18 

(t 

9- 

1.  If  you  have  12  peanuts,  how  many  cau  you  eat 
and  have  9  left  ? 

2.  Fourteen  pencils  less  9  pencils  are  how  many  ? 
14  slates  less  8,  are  how  many  ?    8  plus  6  ? 

3.  If  you  have   15  cents,  how  many  can  you  spend 
and  have  9  left  ? 

4.  William  had  16  cherries  upon  his  tree,  and  the 
birds  took  all  but  9  :   how  many  did  they  take? 

5.  Sarah  bought  15  pink  roots,  9  of  which  died:  how 
many  lived  ? 

6.  A  farmer  had  14  cows  in  a  pasture,  9  of  which 
broke  out :  how  many  remained  in  the  pasture  ? 

7.  What  is  the  difference  between  9  and  13?    How 
many  must  be  added  to  9  to  make  13  ? 

8.  James  saw  18  butterflies  upon  a  bed  of  flowers, 
and  caught  9  of  them :  how  many  flew  away  ? 

9.  There  are  15  sheep  in  a  pasture:  9  of  which  are 
white  and  the  rest  black :  how  many  were  black  ? 

10.  Express  the  following  in  figures:   Two  thousand 
and  ten,  Forty-five  thousand  six  hundred. 

Copy  and  subtract  the  following : 

(ii.)     (12.)     (13.)     (14.)     (IS-)     (16.)      (I7-)     (18.) 

12         13         15         16         14         17         18         19 

99999999 


3S  l»  T  It  A  i  •  T  I  1 1  s  . 

LESSON     X . 

Oral    Drill. 

1.  Ten  from   u   leaves  how  many?     10  from 

10  from  31  ?    10  from  41  ?    10  from  51  ?    10  from  61  ? 
10  from  71  ?     10  from  81  ?     10  I'mm 

2.  Ten    from    12    leaves  how  many:'     10   from 

10  from  32?     10  from   42?     10  from  52?     10  from 
i  72  ?     10  from  82  ?     10  from  <, 

3.  Ho\v  many  are  13  less  10?     23  less  io  ?     33  less 
10  ?     53  less  10  ?  . 

4.  How  many  ore  24  less  10?    44  less  10?    64  less 
10  'i     34  less  10  ?     54  less  10  ?  • 

5.  How  many  are  15  less  10?    45  less  10?     25  less 
10?     55  less  10?     35  less  10  ?  < 

6.  How  many  are  16  less  10?     36  less  10?     5'- 
10  ?    46  less  10?    66  less  10  ? 

7.  How  m:my  an-  17  less   io?     37  less  10?     27 
10?     47  less  io?     67  less  io  ?  • 

8.  How  many  are  18  less  10  ?    38  less  io  ?    28  less 
io  ?     48  less  io  ?    68  less  io  ? 

9.  How  many  are  19  less  io  ?    39  less  io  ?    59  less 
io  ?     29  less  io  ?     49  less  io  ?  • 

10.  How  many  are  20  less  2?    30  less  2  ?    40  less 
2  ?    50  less  2  ?     60  less  2  ?     70  less  2  ?  etc, 

11.  How  many  are  io  l-ss  3  ?   30  less  3  ?   20  less  3  ? 
40  less  3  ?    60  less  3  ?     50  less  3  ?  etc. 

12.  How  many  are  io  less  4  ?    30  le-s  4?    20  less  4? 
50  less  4  ?     40  less  4  ?     60  l.^s  4  ':  etc, 

(For  explanation  of  terms  in  Subtraction,  sec  p.  60 


SUBTRACTION.  39 


LESSON     XI. 

1.  How  many  are  10  less  7  ?     30  less  7  ?     20  less  7  ? 
40  less  7  ?    60  less  7  ?    50  less  7  ?  etc. 

2.  How  many  are  10  less  8  ?    30  less  8  ?     20  less  8  ? 
60  less  8  ?    50  less  8  ?     70  less  8  ?  etc. 

3.  How  many  are  10  less  9  ?     30  less  9  ?     20  less  9  ? 
40  less  9  ?     70  less  9  V     50  less  9  V  HI-. 

4.  12  less  3  are  how  many  ?     22  less  3  ?     32  less  3  ? 

42  less  3  ?     52  less  3  ?     62  less  3  ?  etc. 

5.  13  less  5  are  how  many  ?     23  less  5  ?    33  less  5  ? 

43  less  5  ?     53  less  5  ?    63  less  5  ?  etc. 

6.  12  less  6  are  how  many?     22  less  6  ?     32  less  6  ? 
52  less  6  ?    42  less  6  ?    62  less  .6  ?  etc. 

7.  14  less  7  are  how  many  ?     24  less  7  ?    44  less  7  ? 
34'less  7  ?     54  less  7  ?     64  less  7  ?  etc. 

8.  14  less  5  are  how  many  ?     24  less  5  ?    44  less  5  ? 
64  less  5  ?     34  less  5  ?    54  less  5  ?  etc. 

9.  1 6  less  8  are  how  many  ?     26  less  8  ?    46  less  8? 
36  less  8  ?    66  less  8  ?     56  less  8  ?  etc. 

10.  15  less  9  are  how  many  ?    25  less  9  ?    45  less  9  ? 

35  less  9  ?     55  less  9  ?     75  less  9  ?  etc. 

1 1.  1 6  less  7  are  how  many  ?     26  less  7  ?     46  less  7  ? 

36  less»7  ?     5 6  less  7  ?     76  less  7  ?  etc. 

12.  15  less  8  are  how  many  ?     25  less  8  ?    45  less  8? 
35  less  8  ?     55  less  8  ?     65  less  8  ?  etc. 

13.  23  less  6  are  how  many  ?    33  less  6  ?    53  less  6  ? 
73  less  6?     63  less  6?     83  less  6  ?  etc. 

14.  17  less  8  are  how  many  ?     27  less  8  ?     47  less  8  ? 

37  less  8  ?     57  less  8  ?     87  Ic.-fi  8  ?  etc. 


NOTATION. 


LESSON    I  . 

1  .  What  in  a  single  thing  called  ? 
A  tt  nit  or  out-. 

1.  What  arc  one  and  one  more  rail*  •<!  '?     "  Two/* 

2.  Two  and  one  more?     "  T! 

3.  Thivi'  ard  one  more?     "Four." 

8.  ^  iie  terms  one,  two,  three,  four,  Ac.? 

>  HIttK'S  Of'  number*. 

3.  What  ia  number? 

y  umber  is  a  unit,  or  a  collection  of  units. 

4.  How  are  numbers  generally  expressed? 
Uy  Figures.  or  L<  ttrrs. 

5.  \Vhut  is  expressing  numben  by  figures  called,  and 
Tin-  Artthic  dotation.     It  ia  so  called,  be- 

cause it  was  introduced  into  Kuroj*-  from  Arabia. 

6.  How  many  figures  does  it  employ? 
The  ten  following: 

I,      2,      3,      4,      5,       6,       7,      8,      9,       o. 

tot,       two,      three,      tar,        five,        six,       KTCO,     eight,      ittt, 


7.  What  are  the  first  nine  called,  and  why  ? 

They  ;in-  ctilhd  sit/n  ijicant  Jiyurcs,  because 
each  always  expresses  a  number. 

They  are  also  called  (lit/  its.  from  digitus,  .-Hii: 

.'ise  the  ancients  used  to  reckon  on  their  lingers, 
§.  What  is  the  last  called,  and  *  1 

\ttu(//it.  Uvunse  when  standing  alone  it  has  no 
value.     It  is  also  culled  zero,  or  n/"' 

9.  How  is  each  of  the  tir<t  nine  numbers  expressed? 
By  a  single  fly  u  re. 


NOTATION.  4* 

LESSON    II. 

10.  What  are  the  first  nine  numbers  called? 

Units  of  the/i/vtf  order;,  or  simply  units. 

11.  What  is  the  greatest  number  expressed  by  one  figure  ? 

Nine* 

12.  How  are  numbers  larger  than  nine  expressed? 

By  forming  other  orders  of  units,  cullnl 

tens,  hundreds,  thousands,  &c. 

13.  How  is  ten  expressed? 

By  writing  i  in  the  second  place,  with  a  cipher 
on  the  right;  as,  10. 

14.  What  are  figures  standing  in  the  second  place,  called? 
Tens,  or  units  of  the  second  order. 

15.  What  is  the  greatest  number  expressed  by  two  figures  ? 

Ninety-nine. 

16.  How  is  a  hundred  expressed  ? 

By  writing  i  in  the  third  place,  with  two  ciphers 
on  the  right;  as,  100. 

17.  What  are  figures  standing  in  the  third  place,  called  ? 

Hundreds,  or  units  of  the  third  order. 

1§.  What  are  the  orders  higher  than  hundreds,  called? 

Thousands,  tens  of  thousands,  hun- 
dreds of  thousands,  millions,  &c. 

1 .  How  many  simple  units  make  one  ten  ?    "  Ten/' 

2.  How  many  tens  make  one  hundred?     "Ten." 

3.  How  many  fojw^rafo  make  one  thousand?  "Ten." 
19.  What  is  true  as  to  the  increase  of  the  orders  of  units  ? 

They  increase  from  right  to  left  hy  the  scale 
of  ten.  That  is,  ten  of  any  lower  order  make  one  of 
the  next  higher  order. 


N  O  T  A  T  1  » 

120.  What  places  do  the  different  orders  ocn. 

^ii/ijiie  units  occupy  tin-  rijht  hand  pi.; 
Tens,  the  second  place ; 
Hundreds,  the  third  pla« 
Thousands,  the  fourth  pi.. 
Tens  of  thousand  fch  place ; 

Hundreds  of  thousand*.  ' 
Mill  inn*,  the  seventh  place,  etc. 
21.  What  is  the  effect  of  moving  a  figure  one  plac* 
right  to  left,  or  from  left  to  right. 

>,v/  ten  tunes  for 
it  is  moved  from  right  to  left;  and  i« 
less  for  every  place  it  is  mo\  ^ht. 

U'2.  What  is  the  rule  for  expressing  numbers  by  figures T 

Begin  at  the  /<//,  m,  \-s  of  ///'• 

yiren  orders  in  their  place*  tfnrurd  the  r, 

If  an  i/ inter  rs  are  omitted,  suj 

place*  with  ciphers. 

Write  in  fiirnrc-  the  following  nuinliers: 

1.  Thirty-seven.  7.  One  hundred  five. 

2.  Sixty-nine.  8.  One  hund. 

3.  Seventy-tl;:  9.  Two  hiuui- 

4.  Eighty-live.  10.  Four  hundred 

5.  One  hundred  two.  u.  Six  hundred  fnrty->even. 

6.  One  hundred  ten.  12.  Eiirht  hundred  seventy-four. 

13.  Fifteen  thousand  and  forty-five. 

14.  Forty-one  thousand  and  ninety-five. 

15.  One  hundred  thousand  and  ti\v  hundr 

16.  Six  hundred  fifty-one  tli.msand  seven  hundred. 

17.  Eight  hundred  forty  thousand  two  hundred  ten. 

1 8.  One  million  two  hundred  ten  thousand. 


NOTATION". 


LESSON    III. 

1.  When  we  designate  objects  as  the  first,  second, 
third,  fourth,  &c.,  what  are  these  terms  called? 

Ordinal  Numbers. 

2.  What  is  the  linger  next  to  the  thumb  called? 
«  The  first  linger."     The  next?     "  The  second  linger." 

3.  The  next?     The  next? 

4.  Beginning  at  the  foot 
of  a  ladder,  what  is  the  low- 
est  round    called  ?     The 
next?     The  next?     The 
next?    The  next?   Wha; 
is  the  top  one  in  this  lad- 
der? 

5.  Beginning  at  thisend 
of  the  class,  name  the  first 
pupil.    The  second.    The 
third.     The  fourth.     Th- 
fifth,  and  so  on  to  the  la>t. 

6.  With   what    regular   number   does    third   corns 
spond  ?     Fifth  V     Seventh  ? 

7.  How  many  tens  in  twenty  ?     In  forty  ?    In  fifty  ? 
In  seventy  ?     In  sixty  ?     In  eighty  ?     In  ninety  ?     In 
?.  hundred? 

Copy  and  read  the  following  numbers  . 

(8.)  (9.)  (10.)  (II.)  (12.) 

534  852  1264  7806  9720 

638  548  3076  8520  9608 

437  659  4275  9067  9999 

739  947  8569  &7°3  .  10000 


NUMERATION. 


LESSON    IV. 

23.  What  'IB  the  method  of  reading  numbers  expressed  by 
ogures.  called  ? 

Numeration* 

21.  Beginning  with  units,  recite  the  table. 


:III.  Period  II.  Period 

*.'».  How  read  numbers  expressed  by  figures? 

Divide  thi-m  hUo  periods  of  three  figures 
counting  from  the  right. 

Beginning  at  the  left  hand,  read  the  p> 
cession,  and  add  the  name  to  each,  except  the  last. 
Copy  and  read  the  following : 

1.  107.  8.  20354.  15.        230684. 

2.  no.  9.  23200.  1 6.  ^007. 

3.  234.        10.  43076.         17.   1000000. 

4.  506.         ii.  50643.         18.   5235640. 

5.  730.        12.  62640.         19.  18642065. 

6.  809.         13.  84063.         20.  81000000. 

7.  943.  14.    97810.  21.    463250648. 

iy  If  this  and  the  next  three  lessons  are  deemed  too  diffi- 
cult for  Deginners,  they  may  be  omitted  till  review. 


ROMAN    NOTATION. 


LESSON   V. 

26.  By  what  other  method  are  numbers  expressed? 

By  the  follow  in  (/  letters,  viz.:  J,  V,  X,  L, 
0,  D,  M. 

JJ7.  What  does  each  of  thea?  letters  denote? 

The  letter  I,  denotes  one ;  V,  five ;  X,  ten ;  L,  fifty ; 
C,  one  hundred;  D,  five  hundred;  M,  one  thousand. 
JJ8.  How  are  other  numbers  expressed  by  these  letters? 

By  repealing   and   combining  them,  as  in   the 
following 

TABLE. 


I          denotes 

one. 

XXIV  denotes 

twenty-four,  &c. 

II 

two. 

XXX 

thirty. 

III 

three. 

XXXI 

thirty  one. 

IV 

four. 

XXXII      •• 

thirty-two,  &c. 

V 

five. 

XL 

forty. 

VI 

six. 

XLI 

forty  -one,  &c. 

VII 

srven. 

L 

fifty. 

VIII 

eight 

LX 

sixty. 

IX 

nine. 

LXX 

seventy. 

X 

ten. 

LXXX      " 

eighty. 

XI 

eleven. 

XC 

ninety. 

XII 

twelve. 

C 

one  hundred. 

XIII 

thirteen. 

CX 

one  hundred  ten. 

XIV 

fourteen. 

CC 

two  hundred. 

XV 

fifteen. 

CCC 

three  hundred. 

XVI 

sixteen. 

CCCC 

four  hundred. 

XVII 

seventeen. 

D 

five  hundred. 

XVIII       " 

eighteen. 

DC 

six  hundred. 

XIX 

nineteen. 

DCC 

seven  hundred. 

XX 

twenty. 

IMVC 

eight  hundred. 

XXI 

twenty-one. 

IXXVC      " 

nine  hundred. 

XXII 

twenty  -two. 

M 

one  thousand. 

XXIII       " 

twenty  three 

MD 

one  thou.  five  liund. 

MDCCCLXXV,  ouo  thousand  eight  hundred  and  seventy-five. 


46  NUMERATION. 

LESSON      VI. 

29.  When  a  letter  is  repented,  what  is  tin'  eff.-rt  ? 

Jfs   eatae  \<  r  Thus.  I  one; 

II,  tw<>:  X,  ti-n  :  XX.  twenty, 

:5O.  If  a  Irtti-r  is  placed  before  one  of  greater  value,  what  is 
the  ell' 

The  value  of  the  less  is  taken   l'n»m  the 

ttl.  Iff.  laced  after  one  of  greater  value,  what? 

The    value  of  the   less   is  ad  fled    t«>  tho 

1.  What  docs  X denote?   1  :-   Whd  XI? 

2.  What  does  V  denote?   WhatlVf    Whd 
32.  II"\v  rxprejw  tlie  numbere  from  10  to  20  by  letters? 

JU  addinf/  the  fetters  d  the  lir.-t  dcc-ade  to 

XL  XI!. 

Express  the  following  numbers  by  letters :  7.  ti, 
i9»  29>  39»  4^»  40,  60,  70,  89,  91,  101,  550,  670,  loio, 


Copy  and  read  the  following  numbers. 


i.   IV. 

\XXIX. 

13-  ( 

2.    VI. 

8.  > 

14.  CCC. 

j,  VII. 

9-  ! 

15.  !>( 

4-    XIV. 

10.  LIX. 

1  6.  MDL. 

5.   XVI. 

II.  I.  XXIV. 

17.  Ml' 

c.   XXIV. 

12.  LXXXV1II. 

18.  .Ml»« 

ll'.l.  In  what  is  t)i«'  Human  N- 

In  e 

into   \vhirh    !•  di\idi-d,   and    in 

hours  mi  ,  and  wat« 


THE     CLOCK. 


LESSON    VII. 

To  Tell  the  Tim*  of  Day  by  the   Clock. 

3  J.  How  is  the  face  of  a  clock  divided  ? 

A  us.    Into   tirdrc    equal    parts    called 
marked  by  the  letters,  I,  II,  III,  etc. 

35.  What  is  the  object  of  the 
two  pointers,  or  hands. 

Ans.  The  short  hand 
tells  the  hours,  and  is  culled 
the  hour  hand ;  the  Io7ic)  one 
tells  the  minutes,  and  is 
called  the  minute  hand. 

1.  When   both    hands    are    at 
XII,  what  time  is  it? 

A/is.  It  is  twelve  o'clock. 

NOTE. — The  teacher  will  explain  that  when  the  minute  hand 

reaches  II,  it  is  ten  minutes  past  one  o'clock  ;  when  it  reaches 

III,  it  is  fifteen  minutes  past  one,  and  while  the  hour  hand 

-  from  XII  to  I,  the  minute  hand  moves  entirely  around 

the  face,  and  points  at  XII,  &c. 

2.  When  the  minute  hand  is  at  VI  and  the  hour  hand  half 
way  between  II  and  III,  what  is  the  time? 

A  HP.  It  is  half  past  two  oV 

3.  When  the  minute  hand  points  at  IX,  what  is  the  time? 
At) a.  It  lacks  fifteen  minutes  of  three  o'clock. 

4.  Where  must  the  hands  be,  to  denote  ten  minutes  past  five  ? 

5.  \Vlu>re  must  they  he,  to  denote  half  past  live'." 

6.  Where  must  they  be,  to  denote  20  minulrs  piist  ei^ht  ? 

7.  When  the  hour  hand  is  past  111,  and  the  minute  hand  is 
nt  V ,  wluit  tin.e  is  it? 

R.  When  the  hour  hand  is  near  VI  and  the  minute  hand  at 
hat? 


ADDITION. 

LESSON    I 

1.  What  is  Addition? 

Addition  is  uniting  two  or  more  numbers  in 

£.  What  is  the  number  obtained  by  addition  railed  '! 

The  Stint  <  r  Amount. 

3.  How  is  Addition  denoted  ? 

By  a  pcrjM'Hflicultfr  cross  called  plus  (4-), 
placed  between  the  numbers  to  be  added.     Thu^. 
expression  4  +  3  shows  that  4  and  3  are  to  be  added 
her,  and  is  read,  "4  plus  3,"  "4  and  3,"  or  ••  4 
added  to  3." 

NOTE. — The  term  plus  signifies  more  or  added  to. 

4.  How  is  the  equality  between  numbers  denoted  ? 
lljtiro  short  /tfiraltel  lutes,  called  the  sign 

of  equality  (  =  ).    The  expression  44-3  =  7,  *••> 
that  4  increased  by  3  equals  7,  and  is  read,  "4  plus  3 
equal  7,"  or  the  sum  of  "  4  +  3  equals 
Copy  and  read  the  following  expressions : 
*•  5+3  +  2+o-H8=  10  +  3  +  5. 

2.  6  +  84-04-9  =  2  +  10  +  3  +  8. 

3.  One  pupil  gave  h<  Cs,  another  8, 
and  another  6:  how  many  peaches  did  a 

SOLUTION. — 7  peaches  and  8  peaches  are  15  peaches,  and  6 
are  21  peaches  :  therefore  all  gave  her  21  peaches. 

4.  If  John  picks  5  roses  from  one  bush,  9  from  an- 
other, and  7  from  another,  how  many  will  In-  pick  ? 

5.  How  many  are  6  quarts,  S  quarts,  and  7  qua. 

6.  How  many  are  18  yards  and  9  yards  and  4  yi 


ADDITION.  49 

LESSON     I  I. 

To     add     single    columns    when    two    or     more    numbers, 
ruining    together,    make    10* 

i.  Find  the  amount  of  5,  6,  3,  7,  8,  4,  6,  9. 

ANALYSIS. — Write  the  numbers  one  under  an-      Operation, 
other,  in  a  perpendicular  column,  and  draw  a  line         5 
under  it.  6 

Beginning  at  the  bottom  and  omitting  the  names  3 
of  the  numbers,  proceed  thus :  Nine,  nineteen  7 
(adding  10  for  6  and  4),  twenty-seven,  thirty-seven  8 
(adding  10  for  7  and  3),  forty-three,  forty-eight.  4 
The  amount  is  48.  6 

NOTES. — i.  When  two  or  more  number?!  to-  9 
gether  make  ten,  instead  of  adding  these  numbers  — 
separately,  it  is  better  to  add  10  at  once.  48  Ans. 

2.  In  all  operations  both  mental  and  slate,  the  pupil  should 
add  each  number  as  a  whole,  and  not  by  single  units,  or  by 
counting  his  fingers.     Counters  should  be  used  no  longer  than 
necessary  to  illustrate  the  different  combinations. 

3.  Great  care  should  be  taken  to  see  that  the  figures  are 
written   with  neatness  and  symmetry,   and  in  perpendicular 
columns. 

Copy  and  add  the  following  in  like  manner : 


(2.) 

(3-) 

(4-) 

(5-) 

(6.) 

(7-) 

(8.) 

(9-) 

8 

4 

3 

9 

4 

7 

6 

8 

2 

6 

2 

4 

7 

3 

9 

7 

7 

5 

6 

3 

2 

6 

8 

9 

2 

2 

4 

2 

3 

4 

7 

6 

3 

6 

3 

8 

5 

5 

2 

8 

7 

5 

7 

6 

8 

2 

5 

7 

6 

5 

5 

3 

2 

3 

3 

8 

6 

3 

6 

2 

3 

8 

6    2 

7 

4 

7 

4 

5 

6 

7 

7 

8 

7 

8 

3 

4 

5 

6 

8 

9 

00  AD  I)  IT  lo 

LESSON    III. 

Mental    Exercises. 

1.  A  teacher  received  6  apples  from  one  of  her  pu- 
pil*, 7  from  another,  and  8  from  another:  how  i 
apples  did  she  receive  from  all  ? 

2.  If  you  pay  10  cents  for  a  slate,  6  cen  i  n  k- 
1,  and  3  cents  for  a  pencil,  how  much  will 

pay  for  all  ? 

3.  If  an  orange  costs  6  cents,  a  pear  5  cents,  and  a 
•umon  4  cents,  what  will  they  all  co 

4.  How  many  are  7  brooms,  3  brooms,  and  8  brooms? 

5.  How  many  are  8  days,  7  days,  and  6  days  ? 

6.  How  many  are  7,  and  6,  and  3  ? 

7.  If  Harry  receives  6  credits  a  day  for  3  days,  how 
many  r'mrks  will  he  IK, 

8.  How  many  are  9  dollars,  6  dollars  and  7  dollars  ? 

9.  How  many  arc  12,  and  ;<,  ami  9? 
Copy  and  add  the  following  : 


w 

W 

(30 

(40 

(5-) 

(6.) 

(8.) 

6 

7 

8 

9 

10 

8 

6 

7 

6 

7 

8 

9 

IO 

9 

7 

9 

6 

7 

8 

9 

IO 

6 

8 

8 

r  6 

7 

8 

9 

IO 

5 

6 

6 

6 

7 

8 

9 

10 

8 

7 

7 

6 

7 

8 

9 

10 

9 

8 

8 

6 

7 

8 

9 

IO 

6 

6 

6 

7 

8 

9 

10 

3 

7 

7 

6 

7 

8 

9 

10 

8 

8 

8 

6 

7 

8 

9 

10 

9 

9 

6 

ADDITION.  51 


LESSON    IV. 

To    add    numbers  consisting    of    two    or    more    Columns, 
when  the   sum  of  each  column  is  less   than  1O. 

1.  What  is  the  sum  of  223,  342,  and  132  ? 
ANALYSIS. — Write  the  numbers  one  under  an-      Operation. 

other,  units  under  unite,  tens  under  tens,  etc.,  223 

and,  beginning  at  the  right,  add  thus  :  2  units  and  342 

2  units  are  4  units,  and  3  are  7  units.     Set  the  7  132 
under  the  units'  place,  because  it  is  units.    Next,  

3  tens  and  4  tens  are  7  tens,  and  2  are  9  tens.    Set  697  A  ns. 
the  9  in  tens'  place,  because  it  is  tens. 

Finally,  i  hundred  and  3  hundreds  are  4  hundreds,  and  2  are 
6  hundreds.  Set  the  6  in  hundreds'  place,  because  it  is  hun- 
dreds. An*.  697. 

(2.)  (3-)  (4-)  (5-)  (6.)  (70 

31  23  24  231  312  413 

24  32  30  324  431  if>o 

II  22  23  132  205  326 

(2.)  (3-)  (4-)  (50  (6.)  (7-) 

25  23  30  231  324  403 
30  42  43  I23  230  232 
24  34  25  404  305  354 

2.  A  farmer  has  two  flocks  of  sheep,  one  containing 
342,  the  other  227  :  how  many  sheep  has  he  ? 

3.  Write  in  columns  and  find  the  sum  of  313  dol- 
lars, 142  dollars,  and  432  dollars. 

4.  James  has  three  books,  one  containing  212  pages, 
another  320  pages,  and  another  456  pages :  how  many 
pages  do  all  contain  ? 


52  A  D  D  I  T  I  O 

LESSON    V. 

To  add   numbers   consisting   of   two    or    more   <  olnmnft, 
when  the  sum  of  a  column   U    1  O.   or  more. 

1.  What  is  the  sum  of  234  dollars,  525 dollars,  and 
443  dollars  ? 

ANALYSIS.— Write  the  numbers  one  under  an-  Operation. 
other,  the  units  under  units,  etc.,  and,  beginning  234  d. 

at  the  right,  add  as  before.    Thus,  3  unite  ar  525  d. 

units  are  8  units,  and  4  are  12  units,  equal  to  I  tea  443  d. 

and  2  units.     Set  the  2  in  units'  place,  because  it 
is  units,  and  add  the  i  ten  to  the  next  column,  be-  Ant.  1202  d. 
cause  it  is  the  »ame  order  as  that  column. 

Next,  i  ten  and  4  tens  are  5  tens,  and  2  are  7  tens,  and  3  are  10 
tens,  equal  to  i  hundred  and  o  tens.  Set  the  a  or  unit's  figure, 
under  the  column  added,  bfcaute  there  are  no  tent,  and  add  the 
i  hundred  to  the  next  column,  because  it  is  the  »ame  order  as 
that  column.  Adding  the  i  hundred  to  the  next  column,  the 
sum  is  12  hundreds,  and  this  being  the  last  column,  we  set 
down  the  v hole  turn. 

NOTE. — As  soon  as  the  learner  becomes  familiar  with  adding 
numbers  which  have  two  or  more  columns,  he  should  on. 
name  of  the  order,  etc.,  and  pronounce  the  results  only,  as  in 
adding  single  columns.    (P.  38,  Ex.  i.) 

2.  What  two  principles  are  necessary  to  be  obs- 
in  addition  ? 

The  numbers  must  he   LiJcr  \ntti  hers. 
2d.   Units  of  the  stimr  nrdrr  mvri  bo  added, 
each  to  each. 

3.  What  are  like  numbers  ? 

Like  lumbers  are  those  which  express  units 
of  the  same  kind;  as,  4  pears  and  3  pears ;  5  and  8,  etc. 

4.  What  are  unlike  numbers  ? 

Unlike  Numbers  are  those  which  express  unit* 
of  different  kinds;  as,  4  dollars  and  3  yarda. 


ADDITION.  f,:j 

LESSON    VI. 

Review   of  Principle*. 

5.  How  do  you  write  numbers  to  be  added  ? 

Write  one  under  another,  units  under  units,  etc. 

6.  When  begin  to  add,  and  how  proceed  ? 

Begin  at  the  right,  and  add  each  column  separately. 

7.  When  the  sum  of  a  column  is  less  than  10,  what  is  doiie 
with  it ;  and  why  ? 

Set  it  under  the  column  added,  because  it  is  the 
same  order  as  that  column. 

8.  When  the  sum  of  a  column  exceeds  9,  what  do  you  do 
with  it  ? 

Write  the  units'  figure  under  the  column  added,  and 
add  the  tens  to  the  next  higher  order. 

f).  What  do  you  do  with  the  last  column  ? 

^'•t  down  the  irhole  sum. 

1O.  How  is  Addition  proved  ? 

Begin  at  the  top,  and  add  each  column  downward. 
If  the  two  results  agree,  the  work  is  right. 

Examples   for   Practice. 

(i.)  ('•)  (3-)  (4.)  (5.) 

233  234  395  382  504 

165  364  265  237  160 

486  246  486  68  439 

283  547  257  385  758 

6.  Find  the  sum  of  305  yds.,  28  yds.,  and  420  yds. 

7.  Find  the  sum  of  325  dols.,  83  dols.,  and  7  dols. 

8.  What  is  the  sum  of  436  4-48  + 1 36  +  20  ? 

c>  What  is  the  sum  of  3450  +  2434- 1789  +  46  ? 


54  ADDITION. 

(10.)                    (II.)                    (12.)  (14.) 

Dollars.                  Fc«t.                     Days.                   Pounds.  Gallons. 

3465      4273       612      7260  8725 

802      6250      7309        39  430 

So^o       367       527       547  57 

2432      5046      6305      9084  5367 

""     ""    ""                                    "                                                                                            "  r 

15.  A  raan  picked  875  oranges  from  one  tree,  739 
from  another,  and  1237  from  another:  how  nuu: 

i<-k  from  all? 

1 6.  One  school  has  475   pupils,  another  630, 

another  568:   ln»\v  many  ]>upil>  i. 

(I7.)        (18.)        (I9.)        (20.)  (21.) 

4358        3460        4504        6720  8354 

754                  58                  75  2075 
5243              8539             7322              5°81 

22.  Find  the  sum  of  275  pounds  -f  468  pound 
723  pounds. 

23.  Find  the  sum  of  463  yds.  +  568  yds.  4-837 

24.  Find  the  sum  of  563  gal.  +645  gal.  -f  750  ; 

(25.)       (26.)       (27.)          (28.)            (29.)  (30.) 

3°    73    3  25    4  84    35  56  67  45 

48    30    4  76    5  40    93  27  90  76 

53    33    8  25    3  33     82  82  38  60 

37  45    7  30    2  22     80  75  54  93 
7-          6  34    3  58     64  40  73  40 
45    64    4  25     7  34     95  67  85  63 

38  7  46     2  76     38  53  64  88 
53    78    5  63    8  43    47  48  90  70 


SUBTRACTION. 


LESSON    I  . 

1.  What  is  Subtraction  ? 

Subtract  lot  i  is  taking  one  number  from  an- 


2.  What  is  the  number  to  be  subtracted  called  ? 

The  Subtrahend. 

3.  The  number  from  which  the  subtraction  is  made  ? 

The  Minuend. 

4.  What  is  the  number  obtained  by  Subtraction  called  1 

The  Difference,  or  remainder. 

1.  "When  we  say,  3  from  8  leaves  5,  which  is  the 
minuend  ?    The  subtrahend  ?     The  remainder  ? 

2.  When  it  is  said  that  6  taken  from   14  leaves  8, 
what  is  the  6  called  ?     The  14?    The  8  ? 

5.  How  is  Subtraction  denoted  ? 

By  a  short  horizontal  line,  (—  )  called 
minus.  When  placed  between  two  numbers,  this  sign 
shows  that  the  number  after  it  is  to  be  taken  from  the 
one  before  it.  Thus,  5  —  3  shows  that  3  is  to  bo  taken 
from  5,  and  is  read  "  5  minus  3." 

IE.  —  The  term  minus  signifies  less. 
Copy  and  read  the  following  expressions  : 

1.  8-3  =  10-5.  4-  "9  —  5  =  "8—  4- 

2.  23-5  =  164-2.  5.   135  +  8=150-7. 

3.  87+4  =  98-7  6.  250  +  7  =  277-20. 

7.  19  dollars—  7  dollars  =  how  many  dollars? 

8.  15  bushels  —  8  bushels  =  how  many  bushels  ? 

9.  23  —  8  =  how  many  ?     27  —  10  =  how  many  ? 


56 


LESSO  Nil. 

ll'hrn  rarh  rifntre  in  the  Lim-rr   \nmber  is 
tlntn   th?  otit-  tihfHT  if. 


i.    Find  the  difference  between  746  and  214. 

ANALYSIS  —  V.  :.•«»  number  under  the     Oper 

greater,  unit*  under  unit*,  tens  under  tern,  • 
Beginning  at  the   ri^bt,  proceed  thus:   4  u 
from  6  units  leavo  2  units.     Set  the  2  in  units' 
place,  under  the  figure  subtracted,  because  it  ia    Ant.  532 
units.     Next,  i  ten  from  4  tens  leaves  3  tens.    Set 
the  3  in  tens'  place.  und«  re  subtracted,  becau 

tfns.    Finally,  2  hundreds  from  7  hundreds!*  dreda. 

Set  the  5  under  the.  hundreds'  column,  because  it  is 

Solve  the  following  in  a  similar  mann< 

(2.)  (3-)  (40  (6.) 

435  546  615  768  879 

312  221  314  544 


(7-) 
575  dole. 
243  dols. 

(8.) 
465  yards. 
234  yards. 

(9.) 
675  days. 
372  days. 

do.) 
4^3 

11.  A  farmer  having  456  sheep,  sold  230  of  t: 
how  many  did  he  have  left  ? 

12.  If  11  ncome  is  685  dollars  a  1  his 

-  are  360  dollars,  how  much  can  he  lay  a] 

13.  What  is  the  difference  between  570  and  340  ? 

14.  What  is  the  dinVn  .oen  700  and  300  ? 

15.  What    is    the    dill'm-mr    lu-twivn    fix    hundred 
forty-five  and  two  hundred  twenty-tlm- 


SUBTRACTION.  5? 

(16.)        (17.       (18.)        (19.) 
456  dols.    564  sheep.    678  feet.    784  pounds. 
324  dols.    234  sheep.    538  feet.    541  pounds. 

(20.)  (21.)  (22.)  (23.) 
5674  7360  8679  9230 
£351  4230  5360  4020 

Mental    Exercise*. 

1.  A  tailor  sold  a  coat  for- 25  dollars,  and  received  10 
dollars  down  :  how  much  is  due  him  ? 

ANALYSIS. — Ten  dollars  from  25  dollars  leave  15  dollars. 

2.  If  you  have   17  doves,  and  sell  8  of  them,  how- 
many  will  you  have  left  ? 

3.  Bought  a  cow  for  35  dollars,  and  sold  her  for  9 
dollars  less  than  cost :   for  how  much  was  she  sold  ? 

4.  A  market  boy  had  44  eggs  in  a  basket,  and  letting 
it  fall  broke  12  :  how  many  remained  unbroken  ? 

5.  William  had  a  25-cent  piece  to  buy  a  lunch,  the 
price  of  which  was  15  cents :  how  much  change  should 
he  receive  ? 

6.  A  young  man  is  21  years  old  to-day:  how  old 
he  8  years  ago  ? 

7.  Nine  and  what  number  are  23  ?      8  and   what 
number  are  32  ? 

8.  7  and  what  are  35  ?    6  and  what  are  42  ? 

9.  Henry  has  10  dollars  in  the  savings-bank  :   how 
many  dollars  more  must  he  get  to  make  50  dollars  ? 

10.  There  are  25  cows  in  a  pasture :  if  9  are  taken 
out,  how  many  will  be  left? 


'•>>  S  U  I)  T  B  A  C  T  I  O  X  . 


LESSON     III. 

JJ7i/'/i  a  Firjiire  in  the  Loircr  \uwber  is  Large* 
t/unt  tht-  our  dltot'f  it. 

i.  What  is  the  difference  1  745  and  438  ? 

ANALYSIS. — Here  8  is  larger  than  5,  and  can-      Oper 
not  be  taken  from  it.     How  is  this  difficulty  re- 
moved ?    There  are  two  method*  438 

ist  METHOD.— We  add  10  to  the  5,  making  15  ; 
now  8   unite  from  15  units  leave  7   units.     Wo    Ant.  307 
write  the  7  in  units'  place  under  the  figure  sub- 
tracted.    To  balance  the  10  added  to  the  upper  number,  we 
add  i  to  the  next  higher  order  of  the  lower,  which  is  equal  to 
added  to  the  upper  number.    Now  i  ten  and  3  tens  are 
4  tens,  and  4  tens  from  4  tens  leave  o  tens.    Place  n 

;  lace,  because  there  are  o  tena.    Finally,  4  hundreds  from 
.Jreds  leave  3  hundreds,  which  we  write  in  hundreds' 
place.    The  remainder  is  307. 

ad  METHOD. — Instead  of  10  taken  at  random,  we  may  take 
i  t< n  from  the  4  trns  in  the  upper  number,  and  add 
units,  making  15.    Now  8  from  15  leaves  7,  which  we  set 
the  figure  subtracted.     Since  we  took  i  ten  from  the  . 

are  but  3  tens  left ;  and  3  t<-ns  from  3  tens  leave  o  tens. 
Finally,  4  from  7  leaves  3.  The  remainder  is  307,  the  save  as 
before. 

NOTE.— The  process  of  adding  10  to  the  upper  figure  is 
commonly  called  "  borrowing  ten." 

6.  What  two  principles  are  necessary  to  be  observed  in 

subtraction  ? 

isi  The  numbers  must  be  L//.V  Xnnihcrx. 
ad.    I'nits  of  the  same  order  must  be  eub- 
tractrd  one  from  the  other. 


SUBTRACTION.  59 


LESSON    IV. 

Review  of  Principles. 

7.  How  do  you  write  numbers  for  subtraction  ? 

Write  the  less  number  under  the  greater,  units  under 
units,  tens  under  tens,  etc. 

8.  Where  do  you  begin  to  subtract,  and  how  proceed  ? 
Begin  at  the  right,  and  subtract  each  figure  in  the 

lower  number  from  the  one  above  it,  setting  the  re- 
mainder under  the  figure  subtracted. 

9.  If  a  figure  in  the  lower  number  is  larger  than  the  ono 
above  it,  how  proceed  ? 

Add  10  to  the  upper  figure  ;  then  subtract,  and  add 
i  to  the  next  figure  in  the  lower  number. 

10.  How  is  subtraction  proved? 

Add  the  remainder  to  the  subtrahend ;  if  the  SUM  is 
equal  to  the  minuend,  the  work  is  right. 


Examples  for  Practice. 

i.  Find  the  difference  between  745  and  280;  and 
prove  the  operation. 


<*•) 

(3-) 

(4.) 

(5-) 

234  dols. 

435  barrels. 

647  gallons. 

730  days. 

1  08  dols. 

260  barrels. 

365  gallons. 

365  days. 

(6-)  (7-)  (8.)  (9.) 

545°  6305  5785  7346 

2237  3252  3060  5037 


S  U  B  T  R  A  C  T  I  O  \  . 


(,0.) 

345  yards. 
1  60  yards. 

,,.) 
520  dols. 
235  dols. 

671  j  >o  unds. 
486  pounds. 

<3-> 

784  quarts, 
92  quarts. 

.MO  ('SO  (16.)  (I7-) 

3427  6504  8050  9650 

1285  4273  437Q 

1 8.  A  farmer  raised  6256  bushels  of  wheat,  and 
3460:  how  much  ;  unsold? 

19.  The  price  of  a  house  is  6475  dollars,  and  tl. 
a  farm  7500  dollars :   what  is  the  different 
prio 

20.  What  is  the  difference  between  five  thou 
and  twenty-five,  and  twenty-live  hundred  and  ti- 

a  i.  What  is  the  difference  between  tea  thousand  and 
-:ul  ten  hundred  and  ten? 

22.  How  many  are  4560  dollars  less  2345  dollars  ? 

23.  Bought  a  lot  of  goods  for   13250  dollars, 
sold  them  for  12500  dollars:  what  was  the  loss? 

24.  63256  —  500200?  27.  710237  —  500420? 

25.  70240  —  43210?  28.  806430—650340? 

26.  85207  —  60340?  29.  900645  —  704306? 

30.  The    population  of   New   York    in    1860  was 
3.880,735;  in  1870  it  was,  4.370,846:   what  was  th 

31.  The  population  of  the  United  States  in   1860 
was  31,443,321 ;  in  1870  it  was  38,312,633:  wh:: 

the  increase? 

32.  A  man  paid  $2500  dollars  for  a  farm,  and  s» 
for  4000  dollars:  how  much  did  he  mak- 


SUBTRACTION.  61 

LESSON    V, 

Oral    Drill. 

To  4  add  6 ;  subtract  3  ;  add  9 ;  subtract  5 ; 
2 ;  subtract  3 ;  add  4 ;  subtract  12  ;  add  8 ;  sub- 
5  :  what  is  the  result  ? 


add  1 2 ;  subtract  3 ;  add  4  ; 
tract  5  :  what  is  the  result  ? 


EXPLANATION. — The  toachor  RRTB,  "  to  4  add  6,"  the  class 
think  10  ;  "  subtract  3,"  the  class  think  7  ;  "  add  9,"  the  class 
think  16;  "subtract  5,"  the  class  think  n;  "add  12,"  the 
class  think  23  ;  "  subtract  3,"  the  class  think  20,  etc. 

2.  From  8  subtract  2  ;  add  4 ;  subtract  5  ;  add  7  ; 
subtract  4 ;   add  2 ;   subtract  5 ;   add  4 ;  subtract  6 : 
result  ? 

3.  To  1 2  add  5 ;   subtract  4 ;   add  6  ;    subtract  8  ; 
add  7  ;  subtract  4 ;  add  7  ;  subtract  6 ;  add  4  :  result  ? 

4.  From  1 3  take  4 ;  add  8 ;  take  5  ;  add  7  ;  take  6 ; 
add  8 ;  take  8 ;  add  7  ;  take  5  ;  add  6  :  result  ? 

5.  From  14  take  7  ;  add  4;  take  3;  add  5  ;  take  9; 
add  6  ;  take  8 ;  add  3  ;  take  4  ;  add  8  :  result  ? 

6.  To  15  add  5;   subtract  6;   add  4;   subtract  7; 
add  6  ;  add  5  ;  subtract  6  ;  add  7  ;  subtract  8  ;  add  9  : 
result  ? 

7.  From  20  take  3 ;  add  8 ;  take  6  ;  add  9  ;  take  8 ; 
add  7  ;  take  9  ;  add  6 ;  take  5  ;  add  6 :  result  ? 

8.  From  34  take  3 ;  add  6 ;  take  10 ;  add  2 ;  take  7  ; 
add  5  ;  take  4 ;  add  9 :  result  ? 

9.  To  17  add  8;  take  6;  add  10;  take  8 ;  take  3; 
add  7  ;  take  4 ;  add  6 :  result  ? 

10.  From  43  take  7  ;  add  4 ;  add  9 ;  take  6 ;  take  5 ; 
odd  10 ;  add  20  ;  take  6  :  result  ? 


MULTIPLICATION. 


LESSON      I. 

To  TK  \rnrw.-The  object  of  (his  Lemon  to  to  dcwfcp  the  MM  of  OHM*, 
as  oMMi  In  Multiplication,  and  lead  the  d*M  to  eee  the  timikrity  of  Multi- 
plication to  Addition. 

1.  Each  pupil  may  make  a  star  or  unit  mark  i 
his  slate,  as  I  make  one  upon  the  blackboard.        :•: 

2.  How  many  times  have  you  made  01. 
Otic  time. 

3.  Make  another  under  the  first  :£ 

4.  H»\v  many  times  have  you  made  i  tt 
Ttro  tunes. 

5.  Make  2  groups  of  2  stars  each;  as,  %  :fc,  ;};  ^:. 

6.  How  many  times  have  you  made  2  mar.. 

times." 

7.  How  many  arc  2  marks  and  2  marks  ? 

marks." 

8.  I  low  many  are  2  times  2  marks?    "4  marks." 

9.  The  m-xt  make  3  groups  of  2  stars  each;  as, 

•fc     2£>  •£    ***>  5JC    2JC. 

10.  How  many  times  have  you  made  2  stars? 
Three  times. 

1 1.  How  many  are  3  times  2  marks  ?    "6  marks." 
i :.  Make  4  groups  of  2  stars  each ;  as, 

<j»    ^jy '  *"{»    rj» »  wj»    rjy »  »J»    5JC  • 

13.  How  many  are  4  times  2  stars?    "8  sUi 


MULTIPLICATION.  63 

LESSON     II. 


2 

time*     I 

are       2. 

2 

times 

7 

«rr 

14. 

2 

"          2 

"       4- 

2 

a 

8 

u 

16. 

2 

14      3 

"       6. 

2 

" 

9 

(4 

18. 

2 

4 

"       8. 

2 

M 

10 

M 

2O. 

2 

"      5 

"        10. 

2 

a 

ii 

(I 

22. 

2 

"      6 

"       12. 

2 

u 

12 

" 

24. 

i.  If  i  lemon  costs  6  cents,  what  will  6  lemons 
cost? 

ILLUSTRATION.  —  Let  the  pupil  place  a  group  of  6  stars 
upon  the  blackboard,  representing  6  cents,  the  price  of  i 
lemon  ;  then  will  2  groups  of  6  stars  each,  represent  the  cost 
of  2  lemons;  as, 


Counting  the  stars  in  these   2  groups  together,  we  have  12 
Btara  ;  hence,  the  cost  of  2  lemons  is  12  cents.     Or,  by 

ANALYSIS.  —  If  i  lemon  costs  6  cents,  2  lemons  will  cost  2 
times  6  cents  ;  and  2  times  6  cents  are  12  cents. 

2.  How  many  are  2  times  4  cents  ? 

3.  Paid  2  dollars  apiece  for  2  caps  :  how  much  did 
both  caps  cost  ?    Show  it. 

4.  How  many  are  2  times  3  fingers  ?    Show  it 

5.  At  6  dollars  apiece,  what  will  2  chairs  cost  ? 

6.  What  cost  2  desks,  at  5  dollars  apiece  ? 

7.  If  you  ride  9  miles  an  hour,  how  far  will  you  ride 
in  2  hours  ? 

8.  What  cost   2   ban-els  of  flour,  at   10  dollars  9 
barrel  ? 


04  MU  LT  I  1'  LI  CAT  I  ON. 

LESSON     III. 


3    times    I    »r« 

3- 

3     times        7     me 

21. 

3      " 

6. 

3      "        8    " 

-4- 

3      "      3     " 

9- 

- 
o                 9 

27. 

3      " 

I  2. 

3      "       10    " 

30. 

3      "      5     " 

'5- 

3      "       ii     « 

33- 

3      "      6    « 

1  8. 

3      "       M    * 

i.  Louisa  bought  3  lead  pencils  at  5  cents  i 
how  much  did  she  pay  for  all  ? 


i  pencil  coat  5  cento,  3  pencils  will  coct  3 
times  5  cento  ;  and  3  times  5  cento  are  15  cento. 

2.  What  will  3  apples  cost,  at  2  cents  apiec 

3.  There  are  3  feet  in   i  yard  :  how  man 
there  in  3  yards  ? 

4.  How  many  are  3  times  3  rabbits  ? 

5.  Bought  3  peaches  at  4  cents  each  :  •••,  i  hey 
• 

6.  If  a  car  goes  6  miles  an  hour,  how  far 
in  3  hours? 

7.  What  cost  3  inkstands,  at^8  cents  ea( 

8.  Paid  7  dollars  apiece  :  was  the 
cost  of  all? 

9.  Henry  has  3  coops  of  9  chickens  each  :  how  i. 
chickens  has  he  in  all  ? 

10.  What  is  finding  the  amount  of  a  number  t 
or  added  to  itself  a  given  number  of  times  cal  : 

Multiplication. 

11.  What  is  the  result  obtained  by  multiplication 
called  ? 


MULTIPLICATION. 


LESSON     IV. 


4  **** 

i    i  -^ 

^    4-^ 

4*A 

•»» 

7  »* 

,28. 

4       " 

2      ' 

*       8. 

4 

a 

8    « 

32- 

4 

*,      ' 
o 

12.         / 

4 

u 

9    " 

36. 

4 

4     ' 

'     1  6. 

4 

" 

10      " 

40. 

4       " 

5     4 

'        20. 

4 

ft 

ii     « 

44. 

4 

6    ' 

'        24. 

4 

u 

12      " 

48. 

i.   \Yhat  i 

is  the 

difference 

in  the 

cost  of  4  pens, 

ccni  •;  apiece 

,  and 

3  lemons 

at  4  cents  apiece  ? 

Iu.i>Ti:.\Tiox.— Let  the  pupil  place  upon  the  board  4 
Croups  of  3  stars  each,  and  suppo>c  them  to  rei>resent  the  cost 
of  4  pears,  at  3  cents  apiece-  :  a.-. 

-::-    -:;•    *  •::•    x    -K-  »  »  #  *   #   *• 

Also,  l>y  3  irroups  of  4  stars  each,  let  him  represent  in  like 
manner  tin-  cost  of  the  lemons;  as, 

v>   •::•   •••   x  x   •::•   •::•   x  x   -::•   «   -::- 

Counting  the  stars  in  theso   ro\vs  M-paratt-ly.  we  find  thsit  each 
rmv  cfjntains  12  stars.      Hence,  4  times  3  cents  is  the  saii,> 
times  4  cents;  consequently  there  is  no  dillen-nce  in  the  cost. 

2.  "What  cost  4  pair  of  boots,  at  5  dollars  a  pair  ? 

3.  If  you  pay  6  dollars  a  week  for  board,  what  will 
i;  cost  you  to  board  4  wee' 

4.  AY h ifh    is    <riv:i(tT,    2    times   6,   or   6   times   2  ? 
Hinw  it. 

5.  What  cost  4  chairs,  at  7  dollars  each  ? 

6.  At  12  cents  each,  what  cost  4  slates  ? 
,'\-  and  multiply  the  following: 

(;-)  -  (9-)  (10.) 

312  521  602  821 

4444 


MI  LTIPLIC  AT  roir, 

LESSON     V. 

5    time.     I     iirr       5.  5    time*       7    «. 

5  10.  5  •     40. 

5  "  3  "  '5-  5  '  9  " 

5  "  4  -  20.  5  "  10  • 

5  "  5  •  5  u  ii 

5  "  6  "  30.  5  "  12  - 


i.  (iooiMjr  ].  blackberries,  and  sold 

them  at  (>  .Mart  :  \\hat  did  they  coinc 

a iv   4  quarts:    h"\v   many  <|iiarl-    in    5 

gftUoi 

What  cost  5  bananas,  at  5  <  h  ? 

4.  (Jeorge  bought  6  kites,  at  5  c  \\hat 

did  lie  nay  l'.»r  tlinn  all  ? 

5.  How  many  l»u>h.-U  cf  a|>plc>  will   5  trees 

v,  mi:  7  bvubell  t" 

hat  CM.-.:  5  f  boots,  at  S  dollars  a  ] 

!l  m  niai 

10  each  d 

8.  AVIiat  is  the  COM  «.f  5  tallies  i\: 

9.  A  furrier  sold  51  how 
much  did  he  i 

10.  IT  n    van!-  of   i  11  make   i   dress,  how 
i.iany  will  he  re-jtiiivd  t<>  make  5  dresses? 

n.  Write  >i\  ihousind.  four  hundred  and  « 
Cojty  and  multiply  the  follow 

(12.)  (i;>.)  (14-)  (15 

410  501  610  700  Si  i 

5  5  5  5 


MULTIPLICATION.  67 

LESSON     VI, 

6    time*    I    are       6.  6    times       7    are    42. 

6         "         2      "       12.  6         "  8      u      48. 

6  "  3  "  1 8.  6  «  9  <•  54. 

6  "  4  "  24.  6  "  10  "  60. 

6  '•  5  «  30.  6  «  ii  «  66. 

6  *  6  "  36.  6  "  12  "  72. 

1.  What  will  6  chair?  cost,  nt  4  dollars  apiece  ? 

2.  Sold  5   quarts  of  cherries,  at  6  cents  a  quart : 
what  did  they  come  to  ? 

3.  If  6  yards  of  silk  will  make  i  cloak,  how  many 
yards  will  it  take  to  make  6  cloaks  ? 

4.  In  i  week  are  7  days :  how  many  days  in  6  weeks  ? 

5.  How  many  Imshels  are  6  times  8  bushels ': 

6.  At  9  dollars  apiece,  what  will  6  desks  cost? 

7.  A  party  of  6  children  gathered  10  quarts  of  nuts 
apiece:  how  many  did  they  all  •rather;' 

8.  A  pleasure  party  hired  6  sail  boats;   each  boat 
carried  n  persons  :  how  many  in  the  party  ? 

9.  How  many  pounds  of  honey  are  there  in  6  boxes, 
it'  each  box  contains  12  pounds? 

10.  What  will  6  penknives  cost,  at  12  cents  each  ? 

1 1.  Write  twelve  thousand,  and  three  hundred. 

12.  Write  ten  thousand,  two  hundred  and  six. 
(    >py  and  multiply  the  following: 

(13.)  (14.)  (I5-)  ('6.)  (n.) 

5111  6llO  7100  8OOO  9010 

66666 


08  II  V  I.  T  I  f LI Ci  T 10 

LESSON     VII. 

;    time*    I    are       7.  7    tluim       ^    are    49. 

7       '  7       "         8    "     56. 

7         »          ;      "  ;  9      »       63. 

7       *•      4     -  7       •        ;o     -     70. 

7      "      5    "     35-  7      "       n 

7       '  7  i-'        . 

1.  1  ..Is  6  pupils  how  n, 

2.  Ai  7  dollar-  ;i  h.ir 

;v  What  cost  7  slates,  at  8 
H..;;I.  r   jui.l    5    9  ill    I 
ii  did  In-  11  ? 

5.  An-  7  tinirs  5  greater  or  less  thau  6  times  7  ? 

6.  If  a  stage  goes  7  miles  an  hour,  how  far  will  it 
.  in  7  ln> 

,v  at    ir   dollars  a  ton: 

8.  How  many  quarts  will  |  hear,  if 

n  10  quarts? 

9.  If  a  v  as  9  dollars  a  week,  how  mud 

,irn  in  7  uci-ks? 

10.  A iv  7  times  7  DUN  |  8  ? 

1 1.  1  7  ni'-loiis  conic  to  ? 
i-'.   il                             i nd.  live  hundred  seventy. 

C  -p.  and  multiply  the  following: 

(I*)  (I4-)  (IS-)  (16.) 

3101  5011  4111  8001  9100 

17777 


M  I'  L  TI  PLICA  T  ION.  09 


LESSON     VI 

8    times     I    are       8.  8    times       "J    are    56- 


8 

M 

2      " 

1  6. 

8      " 

8 

a 

64. 

8 

" 

3    "' 

24. 

8      « 

9 

" 

72. 

8 

(( 

4    " 

32- 

8      " 

10 

ii 

80. 

8 

" 

5    " 

40. 

8      <* 

ii 

« 

88. 

8 

it 

6    " 

48. 

8      « 

12 

« 

96. 

1.  What  cost  8  quarts  of  cider,  at  4  cents  a  quart? 

2.  If  5  school  days  constitute  a  week,  how  many 
school  days  are  in  8  weeks? 

3.  George  spent  6  cents  a  day  for  his  lunch :  how 
much  did  he  spend  in  8  days  ? 

4.  Sold  7  barrels  of  flour,  at  8  dollars  a  barrel :  what 
did  it  come  to  ? 

5.  What  cost  8  yards  of  cloth,  at  8  dollars  a  yard  ? 

6.  Are  8  times  5  more  or  less  than  6  times  7  ? 

7.  In  i  mile  there  are  8  furlongs :  how  many  fur- 
longs are  there  in  9  miles  ? 

8.  If  8  young  peach  trees  bear  10  peaches  each,  how 
many  will  all  bear? 

9.  A  teacher  has  8  classes  in  her  school,  with   n 
scholars  in  each  class :  how  many  pupils  has  she  ? 

10.  Which  is  greater,  8  times  9,  or  6  times  12  ? 

IT.  Write  two  hundred  and  ten  thousand  and  seven. 
Copy  and  multiply  the  following  : 

(12.)  '    (13.      (.4.)      (IS-)      (i<5.) 

5100      7010      6110      8011      9111 

88888 


70  •;  r  L  T  i  i>  1. 1  <  ATI" 

LESSON     IX. 

9    tlmm     I     are       9.  9    times       J    arc    63. 

9  «  2  *  1 8.  9  "  8  u  72. 

9  *  3  "  27-  9  "  9  "  8'- 

.>  "  4  "  36.  9  "  10  "  90. 

9  "  5  «  45.  9  «  !  i  ••  99. 

9  «  6  «  54.  9  "  12  "  »°S- 

T.    h»  i  yard  an-  ;,  l'.-i-t  :  h<>\v  many  i\ct  in  9  yards  ? 

2.  What  cost  4  tables,  at  9  dollars  each  'i 

3.  lln\v  far  will  u  boat  sail  in  9  hours,  if  she  sails  5 
miles  an  hour? 

if  a  liuntiT  kill-  6  pigeons  at  a  shot,  how  many 
will  he  kill  by  9  shots? 

5.  What  cost  9  barrels  of  nnts,  at  7  dole,  a  barrel  ? 

6.  Paid  9  cents  apiece  for  8  inkstand-  :  what  ilM 
they  all  come  to  ? 

7.  What   i.s  tlu-  diflV:  n  9  times  6  ai 
-  8? 

8.  At  10  cts.  a  quart,  what  cost  9  quarts  of  berries  ? 

9.  In  i  dollar  there  are  10  dinu-.s:  lu»w  many  d 
are  there  in  9  dollars  ? 

10.  Charles  obtained  9  merits,  ainl 

for  each  nierr  b  did  he  ' 

ir.  Which  i.-1  crivater,  9  times  8,  or 
12.  \\  ;    .  one  hundred  and  six  thousa; 
Copy  and  multiply  the  following: 

13-)    '  '4')  •    (15)  (i 6-) 

6101  5001  Son  9111 

9999 


A  T 

ION. 

u 

N 

X  . 

IO 

fillies 

7 

are    70. 

10 

» 

8 

"      80. 

10 

(( 

9 

"      90. 

10 

(( 

10 

"    100. 

10 

u 

II 

"     I  10. 

IO 

It 

12 

"    120. 

IO    times     I     are     IO. 

10          k>          2       "        20. 

10  «  3  "  30. 

10  '•'  4  "  40. 

10  "  5  <•'  50. 

10  "  6  "  60. 

1.  What  cost  10  tons  of  coal,  at  6  dollars  a  ton  ? 

2.  At  10  cents  a  yard,  what  cost  7  yards  of  muslin  ? 

3.  If  a  man  earns  10  dollars  a  week,  how  much  will 
he  earn  in  8  weeks  ? 

4.  At  10  dimes  each,  how  many  dimes  in  9  dollars  ? 

5.  What  is  the  cost  of  10  tables,  at  10  dollars  api- 

6.  At  12  dollars  apiece,  what  cost  10  overcoats  y 

7.  How  many  bushels  shall  I  have  from  10 
trees,  if  each  tree  bears  1 1  bushels  ? 

8.  Write  eight  hundred,  and  multiply  it  by  10. 

LESSON     XI. 


1  1  1 

times    I 

are    II. 

I  I    time*       7 

are    77. 

1  1 

- 

"       22. 

ii       -         8 

"     88. 

II 

-      3 

"       3> 

ii       "        9 

"     99- 

1  1 

-       4 

"       44- 

II          "          10 

"     I  10. 

II 

-      5 

"    55- 

ii       •'•       ii 

'*     121. 

II 

"      6 

"     66. 

II          "          12 

"    132. 

1.  A  farmer  sent  1 1  chickens  to  market,  each  weigh- 
ing 3  pounds:  how  many  pounds  did  they  all  weigh  ? 

2.  What  cost  1 1  thimbles,  at  4  cents  each  ? 

3.  At  6  cents  each,  what  will  1 1  tops  come  to  ? 


n 

4.  What    et  <t    i  i    }><)iind>   of    | 
pound? 

5.  JIow  mai  there    in   an   oivhaid. 
which  has  7  rows  and  n    treo  in  a  : 

6.  If  i  melon  is  worth  8  peaches,  how  many  pea 
i  melons  worth  ? 

;.    It'  \<>u  \v  ]•'.!.•  <}  lines  each  d;:y.  how  many  wiK 

in  ji  da 
8.  At  12  cents  a}>  d  \\ill  u  knives  cost? 

LESSON     XII. 

12    time*     I    are     I  J.  iimr*       7    are    84. 

u       "       ->     -     24.  12  8    *•     96. 

I  2          -  ^       -        36.  I  .'          "  Q        '      ! 

I  2          "          .}       •'  12         **          ID      *     120. 

12          -          5       *        60.  '•  I  I 

12        **       6  i  2  i  '      '  '     ; 

1.  William    lia->   5    inarhlrs  and  .I:nn<<  In-    . 

•iy  :    hn\v  niaiiv  ni:irl<les  has  Jan 

2.  How  many  roses  will  4   liii-lu-  j>r.'<hic(\  if 
has  12  roses? 

is  a  mile,  what  will   it  cost  to  rid 


4.  At  7  dollars  a  week,  how  mm-h  will  a  man  FJ- 
in  12  weeks? 

5.  In  i  dozen  there  arc   T:   units:  how  many  units 
an.  there  in  9  dozc'n  ? 

6.  What  cost  TO  dozen  eggs,  at  12  cents  a  do/en  '?     \ 

7.  A  car  ha<  s  wheels:  how  man\  to  •  train 


M  T  J.  T  I  P  I.  I  C  A  T  ION.  ?.'] 

LESSON      XIII. 

Explanation    of    Terms* 

1.  What  is  Multiplication  ? 

Multiplication  is  finding  the  amount  of  a 
number  taken  or  added  to  itself,  a  given  number  nt 
times. 

2.  What  is  the  number  to  be  multiplied,  called  ? 

Th<    Mnlfipficftnd. 

3.  What  the  number  by  which  you  multiply? 

The  Multiplier  ;  and  shows  bow  many  times  the 
multiplicand  is  to  be  taken? 

4.  What  in  the  number  obtained  by  multiplication  called? 
The   rroditcf. 

When  it  is  said  that  2  times  3  are  6,  which  is  tin* 
multiplicand?     The  multiplier  ?    The  product? 

3.   What  el-^e  are  the  multiplier  and  multiplicand  called? 


K  F.MARK.  —  The  product  is  the  xam<  in  whatsoever  order  the 
factors  are  multiplied.  Thus,  if  4  be  represented 
by  a  hori/ontal  row  of  4  counters,  and  3  by  a  +•  4-  +  -f 
perpendicular  row  of  3  counters,  it  is  plain  by  4-  +  +  + 
inspection  that  the  horizontal  row  taken  3  times  +  +  4-  't- 
is equal  to  the  perpendicular  row  taken  4  times. 

(>.  How  is  Multiplication  denoted? 

By  an  ohfiffite  rross,  called  the  *ign  of  nnd- 
'iplicvi'iun  (  x  ).  Thus,  3x4  shows  that  3  and  4  are  to 
•e  -multiplied  together. 

Read  the  following  : 

2x4  =  6  +  2.  4  times  6  =  3  times  8. 

3x6  =  2/9.  3  times  12  =  6  times  6. 


M   t 


M.  iitnl    Rxerciae*. 

1.  What  cost  5  oranges,  at  4  cents  each  ? 

M.YSIS  — If  i  orange  costs  4  cents,  5  oranges  will  cost  5 
4,  or  20  cents.     Therefore,  5  oranges  will  cost  20  n 

2.  What  will  4  pears  <  tfl  cadi  !' 

3.  If  John  \  a  day,  bow  m. 

he  write  in  5  «i 

4.  What  cost  7  writing  books, 

5.  At  6  dollars  aj»i« •« r,  what  cost  8  h;r 

6.  What  c'o-t  9  cloaks,  at  10  dollars  apiece? 

7.  What    i-  the  diJleiviif- 
times  6? 

8.  If  i   orange  is  worth    f>   ai'pl' -.  h«»w  many  ;: 

an-  12  onmgei  vo 

LESSON     XIV. 

99'/u-ii   t/if   Mn/fij:'i>  r  fi<t*  luit  ttti.  .  ami  the 

1'riHluct  <»f    tin  It    /it/ii  rr    i*    /.<>*  than    J(t. 

i.  If  i  car  costs  1304  dollars,  what  will  2  cars  cost  ? 

••  i. YSI*..— \Yriti-    the     niultiplirr    under    tin-      ' 
multiplicand,  an«l  Ix-iriiinin^  at  tin-  oed 

thus:  2  times  4   unit*   are   8   unit-  >  in 

-'ire  inultiplii-d.  beca 

it  i*  unil*.     2  t  9et1  ^6c8 

in  t'-ns'  jilace.  !>• 
3  hundreds  an-  6  In.  n  hundreds'  pla' 

2  t'niH-s  T  Ksand.     Set 

tlu-  2  in  thousjr  etc 

(O  (3-)  (4.)  (5.) 

3.?    -4                         :°2                    22210  3°302 
3                  4 


M  r  LT  [PLIC  ATI  o  N  .  ;:> 

Mental     K\<  r<  is»  ... 

1.  What  18  the  cost  of  7  books,  at  6  dollars  each  ? 

ANALYSIS. — Since  i  book  costs  6  dollars,  7  books  wil»  cost  7 
times  6,  or  42  dollars.     Therefore,  7  books  cost  42  dollars. 

2.  What  cost  6  barrels  of  peas,  at  9  dollars  a  barrel  ? 

3.  How  many  are  8  times  9  horses  ? 

4.  At  7  dollars  a  yard,  what  cost  8  yards  of  cloth  ? 

5.  If  a  pigeon  flies  7  miles  an  hour,  how  far  will  it 
fly  in  ii  hours  ? 

6.  What  cost  9  pounds  of  ham,  at  12  cents  a  pound  ? 

LESSON     XV. 

When  the  Multiplier  li«s  but  otie  figure,  find  the 
Product  of  <t  Jif/ure  is   1O  or  more. 

i.  What  will  3  pianos  cost,  at  536  dollars  apiece  ? 

ANALYSIS. — Since  i  piano  coats  536  dollars,  3          Operation. 
pianos  will   cost   3  times  536  dollars.     Set  the  536  dols. 

multiplier   under  the  multiplicand,  as  before,  3 

and  beginning  at  the  right  proceed  thus  :  3  times 
6  units  are  18  units,  equal  to  i  ten  and  8  units.  Ans.  1608  dols. 
Set  the  8,  or  units'  figure,  under  the  figure  by 
which   you  multiply,  and  add  the  i  ten  to  the  product  of  the 
next  figure,  as  in  Addition.     Again,  3  times  3  are  9  tenn,  and  i 
ten  make   10  tens,  equal  to  i  hundred  and  o  tens.     Set  the  o 
in  tens'  place,  and  add  the  i  to  the  product  of  the  next  figure. 
Finally,  3  times  5  hundreds  are  15  hundreds,  and  i  will  mako 
16  hundreds.     Therefore,  3  pianos  will  cost  1608  dollars. 

Multiply  the  following  in  like  manner : 
(2-)  (3-)  (4.)  (5-) 

4568  37°56  3°74o  64346 

2345 


,  T  i  r  i  i  <  A  T  i 


5°738 

4  6 


(II.)  (12.) 

65327                  548064                       7603 
7  8  9 

14.  In    i    year  il.  :    how  many 
an-  th«Te  in  14  VIM 

15.  If  i  rth  450  d 

;  Hinilar  h  'i  -"5°  dole. 

1 6.  In   i  farm  tl.  ^20  acres  : 
are  I 

17.  What    are    6    carriages  worth,  at   750  dollars 
;q»i-  •« 

18.  Multijily  720;^  ]M)und.s  by  7. 

19.  Multijily  S2oo  <l«)llars 

20.  Multiply  Q.V15  l.arn-N  ],y  9. 

MeutMl      F.xvrrUr*. 

T.   What  is  tljc  price 

ANAI  v-i  :u»l   ?  iiiii: 

s,  or  90;  and  3 

»-«|iml  to  i  ten  and  5  units,  whirh  mldrd  to  i/>  dollars  make  105 
il«illarj«.  the  answer  n-tjuired. 

I.    What  0  M  2  nu'ltulroiH.  at  ;'>  dollar- 

3.  How  many  jNuinds  aiv  4  times  5'>  IN  muds? 

4.  How  many  ^allfii-  aiv  5  tiim-  6;,  -allni 

5.  At  8l  \vliat  will  l.o  the  cu-t  «  f  6 


M  T  L  T  I  I'  L  I  C  A  T  I  O  X  .  77 

LESSON     XVI, 

When  tin-   Multiplier  ling   two   or  more   Figure*. 

i.  Wluit  will  104  horses  cost,  at  245  dollars  apiece  ? 

ANALYSIS. — Since  i  horse  costs  245  dollars,          Operation. 
I-J4  horses  will  cost    104   times   245  dollars.  245 

Write  the  multiplier  under  the  multiplicand,  104 

units  under  units,  etc.,  and   beginning  at  the 
right  as  before,  proceed  thus:  4  times  5  units  980 

are  20  units,  or  2  tens  and  o  units.     Set  the  o,  245 

or  units'  figure,  under  the  figure  by  which' we 
are  multiplying,    and    add  the   2  or  tens   to  Ant.  25480  dels. 
the  next  product.     Tin-  other  figures  of  the 
multiplicand  are  multiplied   by  4,  and  the  results  set  down  in 
like  manner.     Next,  the   product  by  o  tens  is  o ;  we  therefore 
omit  it. 

.»in,  i  hundred  times  5  units  are  5  hundreds.  We  set  the 
5.  or  units'  figure,  in  hundreds' place,  under  the  figure  by  which 
\ve  are  multiplying,  because  it  is  fmmlml*.  The  other  figuren 
of  the  multiplicand  are  multiplied,  in  like  manner.  Finally, 
adding  these  partial  product*  together,  the  result,  25480  dollars, 
is  the  whole  product  required. 

I  I.  What  is  m«-ant  by  partial  products,  and  why  so  called  'i 
I'fd'tlffl  ProtltH'ts  are  tin*  srrrru/  ir^nl/*  which 
arise  from  multiplying  the  multiplicand  by  the  respect- 
ive  figures  of  the  multiplier,   and    arc  so  called    be- 
cause they  are  pnrt*  of  the  entire  product. 
Multiply  the  following  in  like  manner: 

(2.)  (3-)  (4.)  (5-) 

534  3215  43°!  53*° 

35  42  54 


M  U  L  T  I  I'  L  1  L   A  T  ION. 

LESSON      XVII. 

1<>  \  i.  \\    of    Pi  iii.  iples. 
I  .V    1 :    \\  \\ ;  T<- numbers  for  mult ii 
Writ  <'  flic  t/nilti/if 

Him'- 

16.  \Vln-n  tin-  multiplier  has  but  one  t:.  red? 

. 

iiiiil/iji<'  i  it,  and  set  dnu'n    the  result 

Addition. 

17.  WIuMi  tin-  inultiplirr  \\s&  two  or  more  figarefl,  how? 

'//'///  ///'•  tan  1  by  each  i 

tij  I  *cf  (If  nre  of  tack  j> 

i»nl    fir  '         ^um 

1%.  IIo\v  i>  !:;iilti|»];«-!itM»n  proved? 
Multiply  thf    ninltijilipr    by   i 

f/i  the  fir  >rk  is  r( 

Exam 

i.  Multiply  65  hy  38,  and  prove  the  operation. 

Multiplicand         65  tm«-  Multiplier  38 

Multiplirr  38  and      65 

520  190 

195  228 

Product  Same  result  as  before    2470 

(3-) 
35670  481.  67086 

75 


MULTIPLICATION.  79 

6.  Allowing  320  acres  to  a  farm,  how  many  acres 
are  there  in  25  farms  ? 

7.  If  i  carriage  is  worth  850  dollars,  how  much  are 
47  carriages  worth  ? 

8.  What  cost  375  acres  at  54  dollars  an  acre  ? 

(9-)  10.)  (u.)  (12.) 

543^5       45467        76734        68659 
64          68          95          84 

(i3.)         (14-         (15-) 

5427         6854        7496 

73          127          234 


(17.)  (18.) 

37610  74063 

307  278 


21.  TIow  many  oranges  will  75  trees  produce,  if  each 
tree  bears  2563  oranges? 

22.  What  is  the  product  of  563  multiplied  by  153  ? 

23.  What  is  the- product  of  1275  into  2°6  ? 

24.  What  cost  367  horses,  at  305  dollars  apiece  ? 

25.  What  is  the  product  of  430  multiplied  by  321  ? 

26.  If  a  railroad  car  goes  at  the  rate  of  288  miles 
per  day,  how  far  will  it  go  in  335  days  ? 

:>7.)  (28.)  (29.)  (30.) 

3205  5°23  6704  7006 

2.\<>  265  405  2613 


Ml  M  T   I,  1   1   I'  1.  I  <    A  T  I   O  N  . 

LESSON     XVIII. 

\Vhrn    lh«      Multiplier    U     10,     100.     1(100,    rfc. 

19.  \Vlmt  is  tho  et!'.  bet  t  »  u  fi 

It    ri'iiiorrs  tin-  1L  . 

h-n   tint I-M.      I'.  IM.  Q  Thu«. 

but  30  d< 

20.  What,  if  :  . 

ritfiir   is  N  //r/v/  //, 

l»v  ico.      'I  .  l»ut   400 

.  .ur  hum; 
i.   V 

U     .:  will  100  ^luwls  CMSt,  at  58  dollars  eu 


>N.  —  58  iloK  x  100=  5800  (1- 
•Jl.  How  multiply  by  10,  100.  looa  etc.? 

are  c  //>///////// 

—To  anna  signifies  to  place  after,  or  01 

3.  How  ma:  :rs  nll«>v, 
3'>j  days  to  a  year? 

4.  What  is  the  pr.ulurt  <>f  4:1  multiplied  by  100  ? 

.   many  an-  icoo  tl 

V    IOOO. 

;.   Kind  tbe  pn>dnrt  of  256  multiplied  by  1000. 
Multiply  43 SS  by  1000. 
Multipl\  i  oooo. 

10.  Multiply  07063  by  10000. 

11.  Multiply  6504  by  100000. 


MULTIPLICATION.  81 

LESSON     XIX. 

When   one   or   both   factors    have  ciphers  on  the  right. 

i.  What  cost  30  city  lots,  at  2500  dols.  apiece  ? 

ANALYSIS. — Since  i  lot  is  worth  2500  dols.,  2500  d. 

30  lots  must  be  worth  30  times  2500  dols  ,  and  30 

2500  dols.  x  30=7500  dols.  

We  multiply  the  significant  figures  25  by  3,  Ans.  75000  d. 
and  to  their  product  annex  as  many  ciphers  as 
we  find  on  the  right  of  the  multiplier  and  multiplicand,  which 
i»  three.    The  result  is  75000  dols. 

22 .  How  proceed  when  one  or  both  factors  have  ciphers  on 
the  right? 

Multiply  the  significant  figures  together  ;  and  to  the 
result  annex  as  many  ciphers  as  arc  found  on  the  right 
of  both  factors. 

(«•)  (3-)  (4-)  (5-) 

42000        3503  32000        8000 

6  200  300  900 


Ans.  252000  Ans.  9600000 

6.  What  is  the  product  of  9000  into  300  ? 

7.  Multiply  365  by  200. 

8.  Multiply  258  by  5000. 

9.  Multiply  3000  by  327. 

10.  Multiply  80000  by  94. 

11.  Multiply  4000  by  3000. 

12.  Multiply  3200  by  5400. 

13.  If  T  acre  of  land  produces  40  bushels  of  wheat, 
•wh.il  will  3000  acres  produce? 


DIVISION. 


LESSON       I. 

To  TBACHXM.— The  deeiffn  of  this  Le»»on  IK  to  tfmtfop  the  MM  of  Km*, 
M  nied  In  /NrMon,  and  tort  the  popU  to  MM  the  rtniferUy  < 


i.   I  li.tv.    i  j>oncils:  if  I  hand  i  of  them  t«- 
many  sliall  1 

j.   If  I  hand  you  another,  how  man 

How  many  times  ha\«-  I    handed  yon  oft 


many  tinu-s  can    i    jM-ncil    In-   taken  f'r 

pone 

5.    Ii  .;    prar-   in  a  tVuit  di>h  :    if  I    take  I  of 

them.  ho\\  many  will  • 

It'  I  take  i  more,  how  mai 

many  tii.  ir  !" 

Tli  /'<•/•  titm  ^. 

8.  How    many  tinu-s   can    i    j  in    $ 

pemf 

9.  How  many  tim-s  i  in  3  '.'     "  .?  times." 

10.  Ih-iv  are  4  apples  :    it'  I    pass  I   t«>  the  first   pupil, 
to  the   second,  i  to  the  third,  and    i    to   the    fourth, 

how  many  times  shall  I  have  passed  an  apple  ? 
n.  How   mnny  will  he   left?      Show  it  with 


DIVISION.  83 

LESSON     II. 

To  TEACHERS.— The  object  of  this  Lesson  is,  to  illustrate  the  forma- 
tion of  the  Division  Table  of  2. 

1.  Let  each  make  two  stars  upon  his  slate  as  I  make 
them  upon  the  blackboard.  ^f    •& 

2.  If  you  take   2  stars  from  2  stars,  how  many  will 
be  left?    "None." 

3.  How  many  times  are  2  stars  contained  in  2  stars  ? 
One  time. 

4.  Make  two  groups  of  2  stars  cadi ;  as, 

~-  •::-        #  x 

5.  If  yon  erase   2  of  these  stars,  how  many  will  be 
left  ?     "^Two." 

6.  If  you  erase  2  more,  how  many  ?    "  None." 

7.  How  many  times  are  2  stars  contained  in  4  stars? 
Ttro  times. 

8.  Make  3  groups  of  2  stars  each ;  as, 

9.  I  low  many  times  are  2  stars  contained  in  6  stars? 

times. 


I.«-t   the  clafs  continue  the   illustration,  and  write  out  tho 
.  as  below. 


2  in     2,     i   tinn«.  2  in   12,  6  times. 

2  in     4,     2  tin  i  2  in   14,  7  times. 

2  in     6,  '  3  times.  2  in  16,  8  times. 

2  in     8,     4  time-.  2  in  18,  9  times. 

2  in   10,     5  times.  2  in  20,  10  times. 

10.  If  Joseph  can   buy  i  pencil  for  2  cents,  how 
m.iny  pencils  can  he  buy  for  8  cents  ? 


LESSON      111. 

3  in  3,  i  i  3  in  18,    6  times. 

3  in  6,  2  times.  3  in  21,     7  times, 

3  in  9,  3  times.  3  in  24,     8  times. 

3  in  J2,  4  times,  3  in  27,     9  tin 

3  in  15,  5  times.  3  in  30,   10  tin. 

i.  II-  .w  in  ;:ny  oranges  at  3  cents  each  can  George 

liny  for  12  ce: 

u/rsis.—Since  3  cento  will  buy  i  orange,  12 
>M  many  as  3  cents  are  contained  times  in  12  cents,  \ 

i  i.«-.-.    'I  ; 


2.  If  3  apples  ;r  i  jviifil, 
are  6  apples  worth!' 

3.  At  3  cents  a  yard,  how  many  yards  of  tape  can 

you  liny  for  9  cents? 

4.  How  many  threes  in  15  ?     In  ?  r  V     In 

5.  How  many  times  can  you   taki-   3  apples  fr«>m  a 
fruit  dish  containing  15  a[  -MO\V  it. 

6.  llo\v  many  n 

7.  What   is  finding  how  many  times  one  numlx-r  id 
containr.l  in  another  called  ? 

Division. 

8.  What  is  the  result  obtained  hy  division  calle> 
The  <>ttotii>nt. 

Copy  and  divide  the  following: 

(9^  (10.)  (II.)  (12.)  (I3.)  14.) 

3)24  -    '  1 


1)  I  V  I  S  I  0  -V  .  Mo 

LESSON     IV. 

4  in  4,  i   time.  4  in  24,  6  times. 

4  in  8,  2  times.  4  in  28,  7  times. 

4  in  12,  3  times.  4  in  32,  8  times. 

4  in  1 6,  4  times.  4  in  36,  9  times. 

4  in  20,  5  times.  4  in  40,  10  times. 

1.  A  teacher  having  12  apples,  divided  them  equally 
among  4  pupils:  how  many  did  each  receive  ? 

ANALYSIS. — Since  12  apples  were  divided  equally  among  4 
pupils,  each  pupil  received  as  many  apples  as  4  is  contaim-d 
tinii-H  in  12  ;  and  4  is  in  12,  3  times.  Therefore,  each  pupil 
iv»  eivrd  3  appi< 

2.  If  you  give  8  marbles  to  4  boys,  how  many  will 
each  receive !' 

3.  Henry  paid  16  cents  for  4  pears:  how  much  was 
that  apiece  ? 

4.  If  you  divide  20  pounds  of  flour  equally  among  4 
persons,  how  many  pounds  will  each  receive? 

5.  How  many  fours  in  16  ?    In  20?    In  24  ? 

6.  Sold  4  vests  for  28  dollars  :  what  was  that  apiece  ? 

7.  A  teacher  bought  4  slates  for  40  cents :  what  was 
the  cost  of  each  ? 

8.  If  you  pay  36  cents  for  4  quarts  of  chestnuts, 
what  will  that  be  a  quart  ? 

9.  How  many  fours  in  36  ?    In  24  ?    In  32  ? 

Copy  and  divide  the  following : 

(10.)   *       (ii.)          (12.)          (13.)          (14.)          (15.) 
4  20  4  32  4  28  4  36  4  24  4  4c 


D  1  V  1  S  1  U  N  . 

LESSON     V, 

5  in  5.  i   ;  5  in  30,  6  times. 

5  in  10,  2  ti,;.  5  ,. 

5  in  15,  3  times.  5  in  40,  8  tin. 

5  in  20,  4  times.  5  in  45,  9  tin; 

5  in  25,  5  times.  5  in  50.  10  times. 

1.  If  you  cKfidi   10  marbles  i  ial  parts,  how 
many  will  tin-re  he  in  each  j>art? 

2.  If  you  pay  15  eeiits  for  5  yards' 
will  thai 

3.  Bought  5  quarts  of  milk  for  20 
that  a  qof 

4.  If  30  children  are  seated  equally  on  5  ben 
how  many  will  there  be  on  a  ben 

5.  If  5  guns  cost  40  d«»llui>.  what  will  i  gun  c<'- 

6.  A  man   having  35  acres  of  land,  fenced   it  into  5 
equal  pasture-:   ho\\  many  acres  to  a  pa 

7.  If  you  walk  45    miles  in  5 
will  you  walk  j 

8.  A  tea  1   50  dollars  in  eqn 

:ig  5  of  his  hi  -  :    what  did  each  r- 

9.  Ayonni:  man  paid  40  dollars  for  boar 
wa<  that  per  week  / 

10.  George  received  45  cents  for  picking  5  quai 
strawberries :  what  was  that  a  quai 

Copy  and  divide  the  following: 

(II.)  (12.)  (I3.)  (14.) 

5)25  5)30  5)35 


DIVISION.  8? 

LESSON     VI. 


6  in     6,     i  time. 
6  in  12,     2  times. 
6  in  1  8,     3  times. 
6  in  24,     4  times. 

6  in  36,     6  times. 
6  in  42,     7   times. 
6  in  48,     8  times. 
6  in  54,     9  times. 

6  in  30,     5  times.  6  in  60,  10  times. 

1.  II mv  many  yard<  of  ribbon  at  6  cents  a  yard  can 
you  buy  for  18  cents  V 

2.  If  you  put  6  oranges  in  a  basket,  how  many  bas- 
kets will  be  required  to  hold  36  oranges  ? 

3.  If  I  pay  12  dollars  for  6  books,  what  will  the 
books  cost  me  apiece  ? 

4.  In  6  pages  the  printer  made  24  mistakes:   how 
many  mistakes  was  that  to  a  page? 

5.  How  many  quarts  of  milk,  at  6  cents  a  quart, 
can  be  had  for  36  cent 

6.  At  6  dollars  apiece,  how  many  muffs  can  be  pur- 
chased with  42  dollars? 

7.  How  many  times  can  you  take  6  marbles  from  4-S 
marbles  ? 

8.  If  Samuel   gains  6  credits  each  day,  how  many 
.vill  it  take  him  to  gain  54  credits  ? 

9.  If  a  man  lays  up  6  dollars  a  week,  how  long  will 
it  take  him  to  lay  up  60  dollars  ? 

Copy  and  divide  the  following : 

(10.)  (n,)          (12.)          (13.)  (14.  (15.) 

6)30  6)24  6i.j2  6)4.^  660  654 


i)  i  v  i  s  i  u  x . 

LESSON      VII, 


7  in     7,     it; 
7  in   14,     2  times. 
7  in   21,     3  times. 
7  in  28,     4  times. 
7  in  35,     5  time* 

;   m  42,     6  timci 
7  in  49>     7   ' 
7   in  56,     8  : 
7  in  63,     9  ; 

7   in   70,   10   ' 

1.  If  7  yards  of  twist  are  worth  21  cents,  f 
yard  worth  ? 

2.  i  -'3  pages  in   7 
pages  will  she  ivad  in  i  day? 

'ns,  how  many  times  7  lemons? 
;    In  7  days  there  is  i  week :  how  many  weeks  in  42 

5.  If  San  ford  shoots  35  squirrels  in  7  days*  how  in 
will  he  shoot  in  i  day  ? 

6.  II- uv  many  sevens  in  63  ?     How  many  in  56?     In 
28?     In  35?     In 

7.  1  >st  56  cents,  h  \\ill 
i  pound  cost  ? 

8.  If  7  loaves  of  bread  will  last  a  family  i 
how  many  \  ill  49  lo;  = 

9.  In  a  peach  orchard  there  are  63  trees  with  7 
in  a  row  :  how  n, 

10.  How  ma:  ;  pencils  make  56 

11.  If  7  dozen  e£<rs  cost  70  cents,  what  cost  i  dozen  ? 
Copy  and  divide  the  following  : 

(12.)         (13.)         (M.)         (15-)         ('*•          («70 

7)21  7)56  7)70 


DIVISION 


:  J 


LESSON      V  I  I  I. 


6  times. 

7  thins. 


8  in  48, 
8  in  56, 
8  in  64, 
8  in  72, 
8  in  80,  10  time.-. 


8  times. 

9  times. 


8  in  8,  i  i. 

8  in  1 6,  2  times. 

8  in  24,  3  tin; 

8  in  32,  4  tiii. 

8  in  40,  5  tii; 

1.  At  8  cents  apiece,  how  many  writing-books  can  be 
had  for  24  cents? 

2.  Ho\v  many  times  can  you  take  8  chairs  from  a 
row  of  32  chairs? 

3.  In  8  quarts  there  is  i   peek  :  how  many  pecks  are 
there  in  40  quart  > ? 

4.  How  many  eights  are  in  56  ?     In  48?     In  64  !- 

5.  How    many  classes  of  8    can    he    formed  of    72 
pupils  ? 

6.  Paid  48  cents  for  6  slates:   what  is  that,  apiece  ? 

7.  A  laundress  paid  64  cents  for  S  pounds  of  starch  ; 
what  was  that  a  pound  ? 

8.  How  many  times  can  you  draw  8  quarts  of  vin- 
egar from  a  <-ask  containing  80  quarts? 

9.  How  many  8-pound  rolls  can  he  made  from  a  ke  ;• 
of  butter  containing  56  pound-? 

to.   William    picked    8   quarts  of   blackberries,  and 
sold  them  for  48  cents:  what  was  that  a  quart  ? 
n.  How  many  times  8  in  32  ?     In  24  ?     In  72  ? 

Copy  and  divide  the  following : 
(12.)          (13.)          (14.)          (15.)          (16.)          (17.) 


8 


8  48 


8'.64 


8)56 


8'' 7  2 


880 


•.Ml  DIV.1SIOX. 

LESSON     IX. 

9  hi     9,     i  time.  9  in  54,  6  times. 

9  in  1 8,     2  times.  9  in  63,  7  times. 

y  in  27,     3  9  in  72,  8  times. 

9  in  36,     4  9  in  81,  9  times. 

nines.  ;n  «,o,  10  times. 

I.    A   teaciier    having    27     pllpiU  Ui: 

•-ua:  ln»w  many  \\eic  in  each  cli 
At  9  doi  is  can  be  had 

dollars  ? 

3.  A  larmer  planted  54  pcat-h  trees  in  9  equal  rows: 
how  many  did  In-  put  in  a  row  ? 

4.  Joseph  rau-ht  45  fish  in  9  hours:  how  many  was 

IT  hour? 

mor  gathered  63  lnislu-ls  <>f  a]  in  9 

trees:  how  many  bushels  did  tin?  a\cra-- 

6.  How  many  times  can  9  be  taken  from  36  ?     1 
45  ?     From  54  ?     l;n>m  63  ? 

7.  If  yon  pay  9  conts  a  quart  for  blackberries.  ho\v 
many  quarts  can  you  i 

8.  If  a  hunter  catches  9  pigeons  at 

h  8 1  pigeons  ? 

9.  At  9   cents  a   pack,   how   many  packs  of 
era*  lit  for  90  cents? 

IQ.  How  many  nines  in  45?    In  36?    11154?    In 

[i*)         ('2-  i.v)        (M-^        ('5-) 

9Uq  9  81  9  72 


DIVISION  HI 

LESSON     X 


10  in  10.     i   time. 
10  in  20,     2  times. 
10  in  30,     3  times. 
10  in  40,     4  times, 
10  in  50,     5  times. 

10  in     60,     6  times. 

10  in     70,     7  time.*?. 
10  in     80,     8  times. 
10  in     90,     9  times. 
10  in   100,   10  times. 

1.  Sarah  paid  40  cents  for  ribbon, which  was  10  cents 
a  yard :  how  many  yards  did  she  buy  'i 

2.  In  10  cents  there  is  i  dime:  how  many  dimes  are 
there  in  60  cents  ? 

3.  It'  you  pay  10  cents  a  mile  fora  horseback  ride, 
how  many  mih-s  can  you  ride  lor  50  cents? 

4.  If  10  chestnuts  arc  worth   i    orange,  how  many 
oranges  are  30  clu-stnuts  worth  V 

5.  At   10  dollars   each,  how  many  aecordcons  can  1  o 
purchased  for  60  dolla; 

6.  How  much  hay.  at  10  dollars  a  ton, can  be  bought 
with  So  dollars? 

7.  How  long  will  it  take  a  horse  to  go  60  miles,  if  In? 
goes  6  miles  an  hour  ? 

8.  Ten  lads  paid  90  cents  for  the  use  of  a  sail-boat  : 
how  much  was  that  apiece  ? 

9.  Ten  dollars  make  i  eagle :   how  many  eagles  in 
100  dol>. 

10.  How  many  tens  in  40  ?     In  50  ?     In  90  ? 

Copy  and  divide  the  following : 

(n.)          (12.)         (13.)          (I4-)          (i5-)          (l6-) 

1060         1050         1070         10)90         10)80         10)100 


1»  1  V  I  <  I  1)  N  . 

LESSON     XI. 

Explanation     of     Term*. 

1.  What  is  1>. 

Dit'ision   is  finding  how  many  times  one  nir. 
U  contained  in  another. 

•2.  What  is  the  number  to  be  divided,  called? 

Diriih'ntl. 

:{.  '!')..•  ftumb  r  to  4h  Uto  by  ? 
Thfl    IHrisrtr. 

4.  v  !ie  number  obtained  1 

Qtiofteftf. 

5.  What  in  tin-  i,umU»r  /</T,  called? 

I  ft  nniitul*  /  . 

\\  IK  n  it  is  said  that  2  is  <  :nul 

i    OfW,  which    i-s   tin-  '     Thf  d  The 

«|U.  :  ivnuiiiidiT  I" 

REMARK. — A  proper  remainder  is  always  lea   than 

6.  I'  <lt'noted? 

I  short  /loriztmtft?  line  Utwecntwo 
(-J-),  called  th     v 

7.  When  placed  between  two  numbers,  what  does  it  H 
I;  number  &v 

hy  the  one  after  if.     Thus,  15  : -3.  >ln»ws  that  15 
IK-  divided  hy  3,  and  is  ivad.  u  15  divided  h\ 
».  How  else  i  n-d? 

By  irrithifj  Ihe  diri-  ;<l<nd  \\\ 

short  lino  hetween  them;  as  -1/. 

,'V  and  read  the  following:  8-7-2  =  4  :    .  4  + 

•S-f-4-4  .-  =  20-4;    V^7  -  6  +  2. 


DIVISION.  03 


LESSON     XII. 

To  TEACHERS.—  The  design  of  this  Lesson  is  to  illustrate  the  (iro  objfrfs, 
or  daises  of  examples,  to  which  Division  it?  applied. 

1.  Charles  has  6  cents  to  buy  apples  which  are  2 
cents  each  :   how  many  can  he  buy? 

ANALYSIS.  —  Since  2  cents  will  buy  i  apple,  6  cents  will  buy 
as  many  apples  as  2  cents  are  contained  times  in  6  cents.  The 
object  here  is  to  find  how  many  times  one  number  is  contained 
in  another. 

Let  the  6  cents  be  represented  by  6  counters  ;  as, 

+       +  +       +  +       + 

Separating  them  into  groups  of  2  counters  each,  we  have  3 
groups.  Therefore,  he  can  buy  3  apples. 

2.  James  has  6  oranges  to  be  divided  equally  be- 
tween his  2  brothers:  how  many  will  each  receive? 

ANALYSIS  —  Since  2  brothers  are  to  receive  6  oranges,  each 
will  receive  i  orange  aa  often  as  2  is  contained  in  6.  The  object 
here  is  to  divide  6  oranges  into  2  equal  parts,  and  find  how 
many  there  are  in  each  part. 

LI  t  the  6  oranges  be  represented  by  6  counters  ;  as, 

+        +        +  +       +       + 

Separating  them  into  two  groups,  putting  i  counter  in  each, 
then  another,  and  so  on,  till  the  counters  are  exhausted,  we 
have  3  counters  in  each  group.  Therefore,  each  brother  will 
three  oranires. 


9.  To  what  two  classes  of  examples  is  Division  applied  '.' 

l-'irst.  Those  in  which  it  is  required  to  find  how 
many  times  one  number  t'.s  contained  in  another.  (See 
examples,  pp.  83,  84.) 

Second.  Those  in  which  it  is  required  to  divide  a 
number  into  equal  parts.  (Sec  examples,  pp.  85,  86." 


LESSON      XIII. 

K. — In  th<  arner 

will  observe  that  tin-  di\  i^-r  and  -ii\  idend  ure  the  same  d> 

i    the  quotient  i>  tiiinf.  or  nn  ,'l'*1r<irt  nun 
In  the  N  ftmil,  tin-  divi.-or  and  dividend  are  different  denom- 
'<*,  and  the  y>i»ti<  >it  IB  the  saiue  denomination  as  the 
The  proceasof  reasoning  in  tl 

!>ut   the  jirnrtiral  operation  is  the  Kam» 
v  //;/<»•/•  one  number  is  contained  in  anotlier, 
\\hich  accords  with  the  definition  of  Division. 

i.    A    i;inn<  I    30    l*>: 

•  ••jually  among  6  lads:  what    part,  ami  !  'i  di«l 

i  latl 

rr,  i    lad    I 
<>f  30  pounds  ;  and  is  5  pounds. 

> bought 
for  20  cents  ? 

>s — Since  5  cents  will  buy  i  \\ 
huy  n^  many  as  5  cents  ar«  i  tiuies  in 

i.i  4  time.-.     Thert-fure.  20  «vnt.<  will  buy  4  whistles, 

3.  To  \\liich  class  does  K  n.i:'/     \\  ; 
2?     Wl.;- 

4.  It'  6  iii.-ii  can  earn    iS   dollars  per  day.  how  much 
can  i  man  earn  in  the  .<am 

5.  At  8  cents  a  <iuart.  ho\v  much    milk  can   be  hail 

nts? 

6.  If  a  teaclirr  having-  60  pupils  puts  12  in  a  class, 
!i!>w  many  classes  will  he  have  ? 

1lo\v  many  drum*,  at  9  dollars  each,  can  )->e  hou-ht 
for  108  dollar 


DIVISION.  0.-) 

LESSON     XIV. 

Slate  Exercises  in   Short   Division. 

i.  How  many  apples,  at   2   dollars  a  barivl,  ran   you 
obtain  for  4602  dollar-  '.- 

ANALYSIS.  —  Write  the   divisor  on  the  left  of      OJH  ration 
the  dividend,  with  a  curve  line  between  them,  and          2)4602 
proceed  thus:    2  is  contained  in  4,  2  times  ;  write 
the  2  under  the  figure  divided,  for  it   is  the  ,«n)tc  Ana,  2301  b. 
or<l'  r  as  that  figure.     Next,  2  is  contained  in  6,  3 
times  ;    write   the   3   under   the   figure    divided,  for   the    same 
reason.     2  is  contained   in  o,  no  times  ;  write  a  cipher  in  the 
«|iiotient.     2  is  in  2.  i  time;    .-ft  the  i  under  the  figure  divided. 

(2.)  (3.)  (4-  (5-) 

2)"420  ^09  48048 


(6.)  (7.)  (8.)  (9. 

6)56o6  7)7070  8)8008  9)9000 

Mental    Exercise*. 

1.  How  many  balls,   at  8   cents,  can   Henry  buy 
for  50  cent?,  and  how  many  cents  will  he  have  left? 

2.  If  you  devicle  54  chestnuts  equally  among  6  of  your 
companions,  what  part  and  how  many  will  each  re- 
ceive ? 

3.  How  many  times  is  7  contained  in  38,  and  how 
manv  over? 


I   V 


LESSON     XV. 

\\luii    lh«     I)i\U«»    in    itnl  .«    «  \ac  M>    m    .    ich     1'ljfur* 

of  Hi.     l)i,i,I. 

i.  Mow  many  yards  of  cloth,  at  4  dollars  a 
a  tailor  buy  for  126027  dull.. 

is. — Since  he  can  buy  i  yard   f«>r  4      ^. 
dollars,  for  126027  dollars  he  can  buy  as  many      4)126027 
yards  as  4  is  contained  times  in  126027. 

ite  the  numbers  and  divide  as  before.         An*.   31506}  y 
But  the  divisor  is  not  contained  in  the  first 
figure  of  the  dividend,  therefore  we  find  how  manv 
contained  in  the  first  is,  4  is  in  12, 3  times.    Set 

iind'T  tin   ri-lit  hand  figure  divided.     Again,  4  is  i: 
and  2  remainder.     Set  the  i  under  the  figure  divided,  and  pre- 

the  remainder  mentally  to  the  next  figure,  mak 
4  is  in  20,  5  times.    Set  the  5  under  the  figure 

t.  4  is   n<  •  d  in  2,  we  therefore  put  a  nphrr  in 

lotient,  an<:  ••  2  to  the  next  figure,  as  if  a  r» 

d«-r.  making  27.     Now  4   is    in  27,6   time's  and  3  reran 
NVritinir  this  last  remaind*  «  the 

•  in. 

Copy  and  divide  tin-  following  in  a  similar  mai; 

(3-)  (4.)  (5-) 

°45  4)56368  6)15006  6)8 

681 1  3001 J 

(70  (8.) 

4)78400  5)60903  6)84500 


DIVISION.  97 

LESSON      XVI. 

Review   of  Principle's. 

10.  "When  the  results  are  carried  in  the  mind,  and  the  qno- 
ily  is  set  down,  what  is  the  operation  called  ? 

Short  J)h'i#ioH. 

11.  How  divide  by  Short  Division  f 

Place  the  divisor  on  the  left  of  the  dividend,  ami 
beginning  at  the  left,  divide  each  figure  lij  it,  setting 
the  result  under  tin-  figure  divided. 

lii.  If  the  divisor  is  not  contained  in  a  figure  of  the  divi- 
dend, how  proceed? 

Put  a  cipher  in  the  quotient,  and  find  how  many 
timr*  /hi'  (liriwr  is  contained  in  the  next  two  figures. 

13.  If  a  remainder  arises  from  any  figure  before  the  last, 
how  proceed  ? 

rrefix  it  mentally  to  the  next  figure,  and  dicide  as 
fofore. 

14.  If  from  the  last,  how? 

Place  it  over  the  divisor,  and  annex  it  to  the 
quotient. 

15.  How  is  Division  proved  ? 

Multiply  the  (liri.^jr  and  quotient  together,  and  to 
the  product  add  the  remainder.  If  the  result  is  equal 
to  the  dividend,  the  work  is  right. 

Examples  for  Practice. 

i.  How  many  books,  at  5  dollars  each,  can  be  ob- 
tained for  18038  dollars  ?  Ans.  3607  and  3  over. 


98  n  i  v  i  >  i  <>  N. 

(3-)  (40  (50 

3)27506  4)60745  5)4i378 

10.  How  long  will  it  take  Julia  to  braid  560  .-• 
hate,  if  she  braids  4  each  day  ? 

11.  If  a  111:111  \\a.  .11  hour,  how  long  w ill 
it  take  him  to  go  i  ooo  miles  ? 

Into  h<>u  many  fields  can  a  form  of  360  acres  be 
led,  each  field  containing  6  acres? 

13.  At  8  dollars  a  barrel,  how  many  barrels  of  ; 

can  IM    ha  1  f.»r  640  dollars? 

14.  In  i  \\n-k  there  are  7  days:   how  many  weeks 
are  in  365  days,  and  how  many  days  ov« 

15.  Divide  54672  by  3.  16.  Divide  45060 
17.  !>i\;.de  60456  by  4.  18.  Divide  72036 
10.  Divide  46075  by  7.  20.  Divide  66408  '• 
•I,               s'373  by  9.  22.  Divide  90457 

23.  A  <  built  5  houses  at  a  <•  !f)55° 

dollars :  what  was  the  cost  of  each  ? 

A  miiKT  sent  40260  pounds  of  coal  to  n 
:  how  many  pounds  was  that  to  a  o 

bought  a  5200  dollars,  and  paid 

in  4  annual  pa\ : 
.  \<ar? 

26.  How  many  mik's   HUM    a  l.!nl    llv  |>,-r  day,  to 
niako  2600  miles  in  8  days? 

27.  If  a  ma.  10  doll;;'  g  will 
it  take  him  1  >  .>i*-nd  ^650  d«>ll.i 


DIVISION.  99 

'•,•  /•'', :..]•:'  '•••' :    • 
LESSON     XVII. 

Slate   Exercises  in  Loug  Division. 

i.  Divide  14120  by  3,  using  Long  Division. 

Div.  Div'd.  Quotient 

First.     Find  how  many  times  the  divisor        3)14120(4706] 
is  contained  in  tin-  first,  or  first  two  figures  12 

on  the  left  of  the  dividend,  and  set  the  quo- 
tient 4  on  the  right,  with  a  curve  line  be-  21 
tween  them.  21 
/.     Multiply  the    divisor    by  this             — 
quotient    figure,    and   set   the    product    12  020 
under  the  figures  divided.  18 

Third.     Subtract  this  product  from  the 
figures   divided.      Fourth.     Annex  to  the  2  Rcm. 

remainder   2,  the   next   figure  of  the  divi- 
dend, making  21  for  a  new  partial  dividend. 

Dividing.  in-fore,   the  third  partial    dividend    is  2. 

But  the  divisor  3  is  not  contained  in  2.  We  therefore  place  a 
cipher  in  the  quotient,  and  bringinir  down  the  next  figure, 
divide  as  before.  Finally,  placing  the  remainder  arising  from 
the  last  figure  over  the  divisor  and  annexing  it  to  the  quotient 
— the  result  is  47063. 

NOTE. — To  prevent  mistakes,  it  is  customary  to  place  a 
mark  under  the  several  figures  of  the  dividend,  when  brought 
down. 

py  and  divide  the  following  by  Long  Division.  . 
(*•)  (3-)  (4-)  (5«) 

43328  3'3564  54570  65256 

'6.)  (^  (8.)  (9.) 

645735  8^56450  7^65384  9' 


I  >  I   V  I  S   i 

LESSON     XVIII. 

Review   of    Principles. 

10.  \Vhen  the  n*uU*ot  the  several  rteps  and  the  qu 
are  all  set  down,  what  is  the  operation  called  ? 


17.  \Vhut  i.s  tin-  fust  step  in  Long  Division? 

rhnl   /tfJtr  nuinii  tinu'x    the   di 

I  in  tlie  fewest  figures  on  the  left  of  the  dividend 
that  will  runt  din  it. 

I  §.  The  second  ? 

Muftijtfu  f/ic  f/i'-fs(u' 
and  set  ///  'ic  figures  divided. 

19.  The  third? 

Subtract  t/tc   j  trot  I  act   from   the  figures  di~ 

4O.  The  fourth? 

AIUH-.I-  remainder  the  next 

for  a  new  partial  dicidcnd  ;  tlicn  divide  as 

V. 

4  1  .  What  is  to  be  don<«  with  the  final  r- 

'he  divisor,  and  annex  it  to  the  </ 

NOTES.—  i.   If  tin-  p*n-i,,f*  of  tv  :igure 

placed  in  t 
quotient  figure  is  too  large,  and  therefore  mupt  i 

2.  If  the  remaindrr  is  ?qn<il  to  or  yreater  t  i»or, 

the  (juoticnt  li.:  it.-  i.s  too  snia  •  t  be  incretued. 

10.   llow  many  tiiiu-  is  15  (•••ntaiiu'd  in  105.- 

AN  limn  -  S  i;.-.    the  divisor  is  not 

tained  in  tin-  fn>t   two  tijrun-s  of  the  divi-      15)10523(701,'^ 
dend.  we   find   ln»w   many  times  it   is  o« 

!    in    the   lii>t  -liat 

\\  1!   mntuin   it  ;    then  inulti]i1\ 


DIVISION.  301 

Examples   for   Prac'lice.'    ' 

1.  Divide  1506  by  23.  Ans.  655*. 

2.  Divide  2536  by  8.  7.  Divide  34568  by  24. 

3.  Divide  3745  by  12.  8.  Divide  44605  by  21. 

4.  Divide  4678  by  15.  9.  Divide  66431  by  32. 

5.  Divide  5168  by  9.  10.  Divide  75054  by  37. 

6.  Divide  6238  by  25.  n.  Divide  96387  by  45. 

12.  A   drover   laid  out   5600   dollars   in   cattle,  at 
25  dollars  a  head :  how  many  did  he  buy  ? 

13.  If  a  man  can  earn  36  dollars  a  month,  how  long 
will  it  take  him  to  earn  432  dollars  ? 

14.  A  man  invested  9765  dollars  in  land,  at  20  dol- 
lars an  acre :  how  many  acres  did  he  buy  ? 

15.  Allowing  63  gallons  to  a  hogshead,  how  many 
hogsheads  can  be  filled  from  a  cistern  holding  7000 
gallons  ? 

1 6.  How  long  will   15000  dollars  support  a  person 
whose  expenses  are  75  dollars  a  week? 

17.  A   captain    distributed    3150    pounds   of    flour 
among  a  company  of  soldiers,  giving  each  45  pounds: 
how  many  were  in  his  company  ? 

1 8.  Allowing  52  weeks  to  a  year,  how  many  years  in 
5252  weeks? 

19.  At  95  dollars  apiece,  how  many  horses  can  be 
purchased  for  9800  dollars  ? 

20.  If  a  person  travels  58  miles  a  day,  how  long  will 
it  take  him  to  travel  3480  miles  ? 

21.  Divide  80045  by  61.       23.  Divide  85784  by  63. 

22.  Divide  75007  by  56.        24.  Divide  90705   by  75. 


10-j  I)  I  V  1 

LESSON     XIX. 

To  find  the   Quotient    Figure   when    th<     Divisor  U 

1.  I>i\i<lr  12328  by  382. 

:  we  take  3  for  a  trial  divisor,  <">;«  rnt ',•>,. . 

H  in  contained  in  12,  4  times.     But  multiply.  382)12328(32 

ing  8  bjr  4,  we  have  3  to  add  to  tin-  ],n*lmt  ..f  1146 
tin-   next   figure,  and  3  added  to  4  times  3, 

make  15,  which  is  larger  than  12,  the  figures  868 

(1.    Hence  4  is  too  Imrp-  for  tin  764 

1..    .:•• 

aiul  proceed  as  before.  Jfem.  104 

•2*2.    How   find   the  quoti.-nt  figure,  when  the  divisor  is 

lurp-  •'. 

Tul  f  figu  re  of  the  divisor  for  a  trial  divisor, 

nd  how  11.  rs  it  is  contained  in  the  first  or 

f  wo  figures  of  the  divid  <lue  aUoir 

for  carnjitxj  the  tens  of  /  the  second  figure 

of  the  divisor  into  the  quotient  f 

2.  Divide  53643  by  213.     5.  Divide  678543  by  503. 

3.  Divide  64078  by  345.    6.  1 

4.  Divide  4384<>  by  456.     7.  Divide  830245  by  2345. 

LESSON     XX. 

When   the   DivUor  i»   10,    1OO,    1OOO, 

i.  Ho\v  iiiaiiy  horses,  at  100  dollars  a]  i  be- 

bouglit  l\»r  1545  dollars? 

g  n  rijilior  fmm  tho  ^y  -iiti--n. 

\  a  MiimlN-r,  <Ii>ide*  it  by  10  ;  for,  earh  i  <x>)i5  45 
liiTun-  in  the  nuiir                 .»ved  one  place 
loth«  ri-l:t.    a\  M.  g  12.)  .  45  ^*». 


DIVISION.  103 

In  like  manner,  cutting  off*  two  figures  from  the  right  of  a 
number,  divides  it  by  100;  cutting  off  three,  by  1000,  etc. 

As  the  divisor  is  100,  it  is  only  necessary  to  cut  oft'  two  figures 
on  the  right  of  the  dividend  ;  those  left,  are  the  quotient,  and 
cut  off,  the  remainder. 


23.  How  proceed  when  the  divisor  is  10,  100,  1000,  etc.? 

/>«//>  the  riijht  of  the  dividend  cut  off  as  many  figure* 
as  there  are  cipher*  in  Ho1  divisor.  The  figure*  left  ici!i 
he  the  <j  >inti<'  tit  ;  ///o.sr  cut  off,  the  remainder. 

2.  Divide  564  by  100.  5.  39467  by  10000. 

3.  Divide  6531  by  1000.       6.  72364  by  100000. 

4.  Divide  8000  by  1000.       7.  200000  by  100000. 

8.  Divide  2354  by  20. 

ANALYSIS.  —  We  cut  off  the  cipher  on  Operation. 

the  right  of  the  divisor,  and  the  figure  4          2(0)23514 
on  the  right  of  the  dividend  ;  then  divide 

by  2,   the  other  figure  of  the  divisor.      Quo't,  117,14  Item. 
The   result,  117,  is   the   rjuotient,  and  4, 

the  figure  cut  off,  being  annexed  to  the  remainder  i,  is  the  true 
remainder. 

21.  How  proceed,  when  the  divisor  is  composed  of  sig- 
nificant figures,  with  ciphers  on  the  right? 

I.  Cut  off  the  ciphers  on  the  right  <>f  the  divisor,  and 
a*  iiiiniy  figures  on  the  right  of  the  dividend. 

II.  Jh'vidc  the  r<'ni<ihihi<i  part  of  the  dividend  by  the 
remaining  part  of  the  divisor  for  the  quotient. 

III.  Annex  the  figures  cut  off  to  the  remainder,  and 
t]n>  res  u  If  a-  ill  be  the  true  remainder. 

9.  Divide  6533  by  20.       n.  Divide  43681  by  210. 
10.  Divide  42345  by  30.     12.  Divide  48642  by  2300. 


In4  li  I  v  I  -  I  c, 

LESSON     XXI. 

Oral    Drill. 

To  TEACHBM.-Bcttcr  remits  will  be  obtained  by  Oral   Drill*,  aftortf, 
and  frtquent,  Uun  from  Korea  of  example*  recited  In 


i    To  3  add  4;  subtract  2  ;  multiply  by  4  :  .!' 
by  2  ;  subtract  4  ;  multiply  by  5  :  divide  by  i 

Ex  i  or.  —  The  teacher  names  the  number  and  the 

operation  to  be  performed  slowly  at  first  ;  the  class  ]- 
operation  mentally.     Thus,  tin-  teacher  says,  "  to  3  add  4,  "  tin- 
class  think  ,«•  class  think  5;  "mult 

the  class  think  20,  and  so  on. 

2.  From  8  take  5  ;  add  3  :  multiply  by  4  :  divi.i 
iiiltiply  by  5  ;  i.ik«-  4  :  divide  by  2  :   result  '/ 
Multiply  4  by  9  :  divide  by  6  ;  add  7  ;  subtract  3  ; 
divide  by  5  ;  multiply  by  8  ;  add  4:  result  ? 

4.  Divide  15  by  3;   multiply  by  ' 
by  9;  multiply  by  8;  add  10  ;  take  5  :  n-sult  ? 

From   15   take   7;    multiply  by  6;   di\ 
add  12  ;  take  3;  add  9  :  by  6  :  result  ? 

6.  To  14  add  6;  divide  by  5:  multiply  by  8;  take 
5;  divide  by  3;  add  3  ;  multiply  by  5  :  result? 

7.  Multiply  7  by  6;  add  8;  divide  by  10;  multiply 
by  7;  t;il  by  3;  multiply  by  8:  r 

8.  Divide   45   by  9  ;  multiply  by  S  ;  take   10:  divide- 
by  6  ;  multiply  by  7  ;  add  10  ;  add  8:  re>ult  ? 

•u   25  take  7;    divide  by  6  :    multiply1 
add  f>  ;    divi.i  :    multiply  by  10  ;    di\ 

multiply  by  20;  divide  by  10;  add  30:   divide  by  8  : 


FRACTIONS. 


LESSON     I. 

1.  If  a  unit  is  divided     m^^^^^m 
into  two  equal  parts,  what 

is  eacli  part  cul, 

One  half. 

2.  If  divided  into  three 
equal   parts,  what   are   the 
parts  called  ? 

Third* 

3.  If  divided   into   four 
equal   parts,  what  are  the 
parts  called  ? 

Jfowrth*. 

1.  Draw  a  line  the  length  of  your  book,  and  divide 
it  into  halves.     Into  thirds.     Into  fourths. 

2.  If  divided  into  seven  equal  parts,  what  are  the 
parts  called  ?    If  divided  into  ten,  what  ?   Into  twelve  ? 

3.  What  is  meant  by  a  half  ?     (See  Q.  i.) 

4.  What  is  meant  by  a  third  ?     Two  thirds  ?     A 
fourth?      Three    fourths?      By  fifths?      Eighths? 

5.  How  many  halves  make  a  unit  or  one  ?    How 
naiiy  thirds?     Fourths?     Sixths?     Tenths? 

6.  What  is  a  half  of  2  cents  ? 

ANALYSIS  —  If  you  divide  2  cents  into  2  equal  parts,  one  of 
pjirts  is  i  cent. 

7.  What  is  a  half  of  4?     Of  6  ?    Of  8  ?     10?     12? 


FRACTIONS. 

LESSON      II. 

i.   What  part  of  2  is  i  ?     "<>,„.  half/' 
B,    What  part  of  $  is  1  ?      "One  third." 

3.  What  part  of  3  is  2? 

ANALYSIS.— Two  b  two  times  i ;  therefore,  two  is  2  times 
i  third,  or  two  thirds  of  3. 

4.  What  part  of  4  is  i  ?     Is  2  ?     Is  3  ? 

5.  Wli;.  5  is  I  I     Of  8J83?     Of  i 

I  divide  6  pencils  equally  among  3  pupils,  what 
part,  and  how  many,  will  each  ; 

ANALYSIS.— <">!  rdof3.    Therefore,  each  v 

i  third  part.     And  i  third  part  of  6  pencil*  ia  2  pen 

7    If  I  di\idc  10  apples  equally  among  5  girls,  \\hat 
part,  and  how  many,  will  each  i 
8.  How  many  hal\«-s  in  tuo  apples? 

ANALYSIS.— In  i  apple  there  are  two  halves,  and  In  2  a; 
there  most  he  2  times  2  halves,  which  are  4  halves. 

9.  How  many  halves  in  4  ?     In  5  ?    In  6?    In  10? 
i  o.  How  many  halves  in  3  and  i  1 
ANALYSIS .— Sim •••  in  nne  there  are  2  halves,  in  3  there  are  j 
times  2  or  6  halves,  and  i  half  will  make  7  halves. 

1 1.  How  many  thirds  in  4  and  2  tli 
i:.   How  many  fifths  in  4  and  3  fit'1 

13.  How  many  units  in  4  hah 

ANALYSIS. — Since  in  2  halv.  -   i   unit,  in  4  halves 

are  as  many  units  as  j   halves  are  contained  times  in  4 
halves,  whirh  i?  2  times.     Ant.  2  units. 

14.  ll..w  many  units  in  6  halves?    In  9  thirds?    In 
8  fourth 


;•  E  ACT  IONS,  107 


LESSON     III. 

Explanation     of     Term*. 

J.  When  a  number  or  thing  is  divided  into  equal  parts, 
what  are  the  parts  callo! ''. 

fractions. 

5.  From  what  do  these  parts  take  their  name  ? 

From  the  number  of  ef/tttt/  parts  into  which 
the  unit  is  divided. 

6.  How  are  fractions  commonly  expressed? 

Hy  jif/ tires  written  above  and  below  a  line,  called 
the  numerator  and  denominator;  as  J,  J,  r7T. 

7.  Where  is  the  Denominator  placed,  and  what  show? 
The   Denominator   is  written  below  the  line, 

and  shows  into  hoiu  many  c^iial  jHtrfx  the  unit  is  di- 
vided. 

§.  Where  the  Numerator,  and  what  does  it  show  ? 

The  Numerator  is  written  above  the  line,  and 
shows  liow  many  jmrf*  arc  expressed  by  the  fraction. 

i.  Express  the  following  fractions  by  figures :  One- 
half,  Two-t  hirds,  One-fourth,  Three-fourths, Four-fifths, 
I -'iv»  --eighths,  Nine-tenths,  Five-thirds,  Seven-fourths, 
]•'«  )iir-tburt  hs,  Twelve-fifteenths,  Nineteen-twentieths. 

(  O))v  and  read  the  following  fractions: 

(»•)         (3-  (4-)  ($.)  (6.)  (7.) 

5          s  »  1          A  4 

i  I  *  '        A 

J          f          A          A          ii          ft 


FRACTIONS. 


LESSON      IV. 

1.  If  George  has  3  half  dollars,  and  his  father  L 
him  2  halves  more,  how  many  dollar*  will  IK-  ha*. 

ANALYSIS. — 3  halves  and  2  halves  are  5  halves ;  and  5  half 
dollars  ure  equal  lo  2  and  I  half  dollars. 

2.  How  inai  Mirths  and  5  i  J  and  J? 

3.  How  many  are  4  fifths  and  ?    Jand}? 

4.  The  price  of  a  top  is  2  and  i  half  cents,  and  that 
of  a  \\histl.-  3  and   i   half  cents:  what  i.-  the  price  of 
both? 

*. — 2  cents  and  3  cents  are  5  cents,  and  i  half  and 
i  half  are  2  halves,  or  I  c<  .  added  to  5  makes  6  cento. 

uy  dollars  are  3  dollars  and  ;,  f  Mirths 
added  to  5  dollars  and  2  f< Mirths? 

6.  If  you  h.  i  give  away  3  fourths  «.f  it, 

how  much  will  you  have  left? 

ANALYSIS.— In  i  ]  4  fourth*-,  n  ml  3  fourths  from 

;th»  leave  i  fourth. 

;.    :     '      I  !'-..m  7  fifths  leave  how  many?     J  fro: 

8.  5  riirliths  from  9  eighths  leave  h<»w  ma;: 

9.  Henry's  1  !   ;  fourths  yards  long, 
and  he   lost    2   and    i    fourth  yards:  how  lor. 

part  left  ? 

A\\I.Y<IS.  —  c  ynnls   from  5   yards  leave  3  yards,  and   i 
from  3  fourths  leaves  2  fourths.     Therefore,  the  part 
l.-ft  was  3  and  2  fourths  yards  long. 

10.  If  you  have   7   eighths  of  a  dollar.  :id  3 
eighths,  how  niueh  will  you  have  1< 


!•'  II  A  <_'  T  1  0  ^  S  .  109 

LESSON     V. 

1.  What  will  4  apples  cost,  at  i  half  cent  each  ? 

ANALYSIS. — Since  i  apple  costs  i  half  cent,  4  apples  will 
cost  4  times  i,  or  4  half  cents :  and  4  half  cents  equal  2  cents. 

2.  What  cost  3  plums,  at  i  third  cent  apiece  ? 

3.  What  cost  8  marbles,  at  i  fourth  cent  apiece? 

4.  What  cost  5  pencils,  at  2  and  i  half  cents  apiece? 
ANALYSIS. — Since  i  pencil  costs  2  and  i  half  cents,  5  pencils 

will  cost  5  times  as  much.     Now  5  times  2  cents  are  10  cents, 

and  5  times  i  h:«.lf  cent  are  5  halves,  equal  to  2  and  i  half 

which  added  to  10  cents  make  12  and  i  half  cents. 

5.  James  bought  6  oranges,  at  4  and  i  half  cents 
eaeh  :  what  did  they  come  to  ? 

6.  How  many  cents  are 4  times  6  and  r  fourth  cents? 

7.  II"W  many  are  8  times  5  and  3  fourths? 

8.  How  many  are  7  times  4  and  3  fifths  ?     6  times 

*j? 

9.  If  a  prar  costs  4  cents,  what  will  i  half  a  pear 
cost  ? 

•  i.Y-qs.—  If  i   pe:ir  f>sN  4  cents,  i  half  a  pear  will  cost 
i  half  of  4  cents,  which  is  2  cents. 

10.  If  you  pay  12  cents  for  a  pie,  what  must  you  pay 
third  of  a' pi'1?     What  is  £  of  12? 

IT.  At  10  dollars  a  hanvl.  what  cost  i  fifth  of  a  bar- 
rel of  flour  ?  What  is  }  of  15  ? 

12.  Charles  gave  3  marbles  to  his  brother,  which 
were  i  half  of  all  he  had  :  how  many  had  he? 

•  LYSIS. — Since  3  marbles  are  i  half  the  number, 2  halves 
mr  the  whole  number)  must  be  2  timca  3  marbles,  which  arc  <> 
marbles. 


11(1  III  ACTION 

LESSON     VI. 

i.  If  2  pounds  of  butter  cost  f  of  a  dollar,  v. 
i  | .mind  cost? 

M.YSIS.  — i  is  i  half  of  2.  therefore,  i  pound  will  cost  I 
half  as  much  aa  2  pounds,  and  i  half  of  J  is  j  of  a  dollar. 

.     If  3  yards  of  muslin  cost  j  of  a  dollar,  what  will 
i  yard  cost?    What  is  J  of  j  ? 

;.   I;  M  luiy  a  pear  for  3  cents,  \vi  of  a 

can  you  buy  for  i  cent  ? 

4.  At  6  dollars  a  yard,  what  part  • 

can  you  buy  f<>r  i  dollar?  ;<  -liars? 

5.  At  4  cents  a  yard,  how  much  elastic  cord  can  I 
luiy  for  5  cents? 

ANALYSIS. —Since  4  cents  will  buy  i  yard,  i  cent  • 
fnurth  of  a  yard  ;  and  5  cents  will  buy  5  times  i  fourth,  i 
arc  5  fourths,  or  i  yard  and  i  fourth. 

6.  At  8  cents  a  pound,  how  much  maple  s 

.id  f»r  i  ;  c.-nts? 

hire  a  barrel,  how  much  flour  can  be 
bought  for  27  dollars? 
8.  If  i  yard  of  braid  cost.- 

v— Since  3  thirds  (i  yard)  cost  6  cents,  i  thir.1 
'Iiirdnf6<  2  cents.     Again,  if  i  third  of  a 

•s,  2  thirds  will  cost  2  times  2,  or  4  cento. 

I :'  i   IH. iiiul  of  almonds  costs  25  cents,  how  nr 
\\ill  £  ,'id  cost  ? 

10.  What  will   ]  of  a  l-arrcl  of  crauhcrrics  « 
at   U  dollars  a  hanvl  ? 


.Virfcel.  Jtronz,. 

UNITED  STATES  MONEY. 


1 .  What  an-  1h<-  denominations  of  U.  S.  money? 
Ku.irlc-.  d«»ll; i r-.  dimes,  cents  und  mills. 

2.  Recite  the  TADLK. 

10  mills  (ni.)     arc 
TO  cents 

10  dimes  " 

10  dollars  " 


i   ecu  I,  rf. 

i  dime,  (/. 

i   dollar,  dol.  or  $. 

i   ca^le,  E. 


100  cents  =  i  dollar;    50  cents  =  £  dollar. 
25  cents       .'.  dollai-:  \2\  cents—  I  dc"ar. 


lit  LTBD     >  T  \  T  i:  B     M  (i  s  L  v  . 

:i.    II'i-.v  arc  tl:«-  <>"in-i  «>f  tli«-  I".  S.  divided? 

Into  y  ins,  and  i  ins. 

4.  Name  the  coins  of  each. 

i.  Tin-  f/otff  t-tthis  are  the  double-ea 
ha[f-  -!»e  </o/for  and    threat 

pieces. 

i  i:    N///VT  COilM 

"v.and  <t 

3.  The  minor  <<>; t,  ^  kA  five-cent  and 

three-cent  j)iece^.  and  the  bronze 

i.  How  i  s? 

ANALTSI>  are  10  cent*  ii.  in  3  dimes 

there  are  3  times  10  ceuts,  which  are  30  <• 

ny  cents  in  4  dimes  ?    In  6 

3.  How  ni;i.  iu  8  dels.?     In  iodol&? 

4.  llou  nianv  liinies  in  40  i-nite? 

is  i  dime  in  10  cents,  in  40 
there  are  as  many  dimes  as  10  cents  are  contained  times  in  40 

!i  is  4  times.    An*.  4  dimes. 

5.  If  y  dimes  in  20  . 

6.  II.. w  many  dollars  in  20  (!'  : 

7.  Ho\v  many  dollars  in  250  cents?     In  45: 
.'».  Il.iw  is  1  .  S.  money  expressed? 

J>»'  ''  of  the  if- 

in'/ h   ///'•  -.    //  the  first 

in-',  places  on  ///'•  /•////// ;  mills  in  the  next,  ami  pa 
(i  mill  in  f/ic  XIIIT*  ,///. 

-  nn-   r\],rr.-sr,!    '  '//  dvllarn,  and 

•linn-*  by  ten*  of  fent*.     Tlius.  5  eagles  ar*  U  $50,  and 

<>  (iiines  as  60  c< 

if  tl»o  inn  expressed 

••ijihtr  must  !>«•  )>rrlix<-d  t«>  it. 


I    N  1  T  K  I)      S  T  A  T  E  S      MONEY.  113 

8.  Write  twenty  dols.,  twenty  cts.,  and  3  mills. 

A  us.  $20.203. 

9.  Write  fifty-six  dols.,  thirty-seven  cts.,  six  mills. 

0.  How  is  U.  S.  money  read? 

Read  the  figures  on  the  left  of  the  decimal  point  as 
dollar*  ;  thw  in  the  first  two  places  on  the  right  a* 
cents  ;  the  next  as  mills  ;  the  others  as  parts  of  a  in  ill. 

10.  Copy   and   read    $78.35  ;    $106.37  ;    $308.735  ; 
$430.064;   $57240;  $60200. 

ADDITION    OF    U.  S.    MONEY. 

11.  What  is  the  sum  of  $20.465;  $6.28;  and  $12  'J. 

ANALYSIS.— We  write  dollars    under  dollars,  $20.465 

cents  under  cents,  etc.,  and  add  in  the  usual  WMV,  6.28 

placing  the  decim<il  jioi/it  in  the  amount  under  12.00 

those  in  the  numbers  added.   (P.  112,  Q.  5.)  


$38.745 
7.  How  add  U.  S.  money? 

Write  dollars  under  dollars,  cents  under  cents,  etc., 
and  add  as  in  simple  numbers,  placing  the  decimal 
point  in  the  amount  under  those  in  the  numbers  added. 

NOTE. — If  any  of  the  given  numbers  have  no  cents,  their 
place  should  be  supplied  by  ciphers. 

(12.)  (I3-)  (14.)  (IS-) 

342.375         460.508          653.36          846.258 

45.26  5°340  40.457  6-°7 

840.385  675.235  892,295  75-345 

1 6.  What  is  the  sum  of  $375.408 ;  $8.254;  $235  ;  and 
$100.40? 


lit  INI  T  i;  i. 

17.  A  man  paid  $5  625  for  a  hat,  $18.50  1 
and  $7.375  for  a  vest  :    \\hat  did  he  pay  for  all !' 

1 8.  taught  a  pair  of  gloves  for  $1.75.  a  tan 
for  $0.87  cents,  and  a  parasol  for  $6..- 5  :    \\  hat  did  she 
pay  for  all  ? 

19.  A  man  owes  $85.08  for  board,  $12.50  fur  1 
and  $58.70  for  clothes :  how  much  does  he  owe  for  all  ? 

SUBTRACTION    OF    U.   8.   M< 

i.  A  man  having  $128.60,  paid  $47.735  1(>r  a  cow: 
how  much  had  he  left  ? 

ANALYSIS. — We  write  the  less  number  under     Optr 
the  greater,  dollar*  '.Ian,  cents  under        $128.60 

cento,  etc.    Subtract  in  the  usual  way,  and  place  47-735 

the  decimal  point  in  the  remainder  under  that  in 

III.-  Mil.trnh. •:»<!.     (P.   112,  Q.  5.)  Ant.  $80.865 

V   How  subtract  United  States  money? 
HV/7'  the  less  number  under  the  greater,  dollar*  un- 
<l>  r  dollars,  cents  under  cents,  etc.,  and  .« 

inbers,  placing  the  decimal  point  in  the  re- 
ider  under  that  in  th*  subtrahend. 

NOTE. — If  either  of  the  pi  von  numbers  has  no  cent*, 
place  should  be  supplied  by  ciphers, 

(*•)  (3-)  (4.) 

>H        $43.605  $107.38  $95.305  $100.00 

35-45  73-625          17-003  10.75 

6.  From  $15.38  take  $12.30. 

7.  IV. >m  $no  take  $68.40. 

8.  A  man  bought  a  horse  for  $250,  and  paid  $118.50 
down:  liuw  much  do<j>  he  -till  owe  f«»r  i 


UNITED      STATES      MONEY.  115 

MULTIPLICATION    OF    U.    S.   MONEY. 

i.  What  will  8  chairs  cost,  at  $12.375  apiece? 

ANALYSIS. — Since  i  chair  costs  $12  375,  8  chains  Operation. 
will  cost  8  times  $12.375.  We  multiply  in  the  $12  375 

usual  way,  and   from  the   right  of  the  product  8 

IK  tint  off  three  figures  for  cents  and  mills,  because 
tin  re  are  three  places  of  cents  and  mills  in  the  Ans.  $99.000 
multiplicand. 

9.  How  multiply  United  States  money  ? 

Multiply  as  in  simple  number*,  and  on  the  r if/hi  of 
the  product,  point  off  as  many  figures  for  cents  (mil- 
mills  as  there  are  places  of  cents  and  mills  in  the  mul- 
tiplicand. 

NOTE. — In  United  States  Money,  as  in  simple  numbers,  the 
multiplier  must  be  considered  an  abstract  number. 

(2.)  (30  (4-)  (5-) 

Mult.     $25.40  $50.625  $9545  $435° 

////  8  9  15  24 


(6.) 

(7-) 

(8.) 

(9-) 

Mull. 

£6207 

$75.835 

$463.05 

$7584-25 

By 

45 

52 

62 

75 

10.  What  will  12  pounds  of  starch  cost,  at  $0.125  a 
pound  V 

11.  At  $0.375  a  pound,  what  will  25  pounds  of  but- 
ter  come  to  ? 

12.  What  will  20  yards  of  cloth  cost,  at  $6.75  a  yard  ? 

13.  A  miller  sold  35  barrels  of  flour  at   $10.50  a 
barrel :  what  did  it  come  to  ? 

14.  What  cost  100  hats,  at  $5.50  apiece? 


116  t   N  i  i  ::  i»  It  Off] 


Of     P.    8,     M<»N  \:\  . 

1.  A  man  bought  6  sleds  for  £21.4;:  \\luit  wa.-  that 
apiece  ? 

ANALYSIS.—  i  Bled  is  i  eixth  of  6  sleds;  therefore,  6)$2i.42. 
i  sled  will  ooet  i  sixth  of  $2142,  which  is  $3.57.       -i»».  $3.57 

10.  How  divide  U.S.  money? 
Divide  as  in  simple  numbers,  <  '.-e  right  ( 

//W/V///  point  off  as  in  res  for  cents  and 

'-re  are  places  of  cents  and  / 

NOTE.  —  For  dividing  money  by  money,  or  by  a  decimal  <li\i- 
eor,  the  learner  is  referred  to  the  Author's  New   i 
•\v  Practical  Arithm* 

2.  Divide  $25.65  by  5.         5.  Divide  $  100.60  by  10. 

3.  Divide  $36.48  by  8.         6.  Divide  $276  b\ 

4.  Divide  $63.72  by  9.         7.  Divide  $360  by  20. 

8.  A  man  sold  7  barrels  of  flour  for  $63.70: 
much  did  be  I 

9.  If  you  pay  $25.74  for  6  yards  of  clotb,  what  will 
that  be  a  yard  i" 

10.  If  I  pay  $14.875   for  7  crates  of  peacht  -.  how 
niiu-h  will  they  cost  me  a  crate  ? 

1  1.  A  bookseller  sold  5  slates  for  $0.685  :  what  waa 
that  apiece  ? 

12.  If  you  divide  $1648  equally  among  4  poor 
sons,  how  much  will  each  receive? 

13.  If  8  yards  of  broadcloth  cost  $56.40,  what  will  i 
yard  cost? 

14.  If  7  pair  of  gloves  cost  $15.75,  what   is   that 
a  pair? 


(.'  OM  I'O  U  X 


T  A  n  L  KS. 


L17 


ENGLISH     MONEY. 
1 1 .  What  are  the  denominations  ? 

Pounds,  shillings,  pence,  and  farthings. 
1  2.  Recite  the  TABLE. 

4  farthings  (qr.  or  far.)    are  i  penny, 
12  pence  "    i  shilling, 

20  shillings  "    i  pound, 


s. 
£. 


. — The  p^ind  sterling  is  repre- 
1  i-nted  by  a  ^old  coin  callfd  a  xvtcrciyn, 
s.ml  its  value  is  414.866?,. 

Tin-  value  of  mi  Knirlish  Milling  is  24.', 
;    and   that    of    a    pinny,    about    2 
cento. 


Sovereign. 


TROY    WEIGHT 
13.  For  what  is  Troy  weight  used? 

For  \vei}jliing//o/(/,  .v//m\ 
I  I.  What  are  the  drinumnations  ? 

Pounds,  ounces,  pennyweights,  and  grains. 

15.   Recite  the  TAIJI.K. 

24  grains  (yr-)        are  i  pennyweiglit,    pwt. 
20  pennyweights     "     i  ounce,  oz. 

12  ounces  "     i  pound,  Ib. 


lb.  oz.  pwt.  pr. 

1.  I  low  many  ounces  in  3  pounds?     In  4  pounds  ? 

2.  In  40  pwt.,  how  many  ounces?     In  42  pwt.  ? 
3    In  2.\  ounces,  how  many  pounds?    In  39 


t!8 


M  ro  i-  N  i.      I  A  i:  ! 


\v  !-;K;  HT. 
Hi.   F..r  \vlmt  H  Avoirdupois  <l? 

'   \Nri-llilii:    ;i  . 

17.  What  are  t  us? 

Tons,  hundreds,  pounds,  and  ounces. 

18.  Recite  the  TABLE. 

16  ounces  (oz.)      are     i  pound,  ll>. 

100  IM.U.  ••      i   hundred  weigl 

20  cwt, or 2000 Ibs., "      i   t<>n.  '/'. 

8  ounces  are  i  pound.    4  ounces  are  ±  pound. 


ih. 


IE — The  onnfe  is  often  divided  into  halt**,  quarters 
In  l)iisiin-<H.  tlu-  f/n/m.  tin-  7'/</r//rof  25  Ibe.,  and  the  /rWn  of 
56  Ibe.,  are  not  used  as  units  of  Avoirdupois  Weight. 

1.  How  many  ounces  in  2  pounds?    In  3  poun 

2.  How  many  ounces  in  2  pounds  and  5  uin 

3.  In  20  ounces,  how  many  pound 

4.  In  32  ounces,  how  many  pound*?    In  42  ounces? 

5.  In  40  hundred  weight.  lu»w  many  t«" 

6.  Il"\v  many  hundreds  in  3  t«- 

7.  How  many  hundreds  ii 


COMPOUND     TABLES. 


119 


APOTHECARIES'    WEIGHT. 

19.  For  what  is  Apothecaries'  Weight  used  ? 
For  nii.riiHj  t/iK/ici/tcx. 

20.  What  are  the  denominations? 

rounds,  ounces,  drams,  scruples,  and  grains. 

21.  Recite  the  TABLE. 

20  grains  (gr.)  are  i  scruple,  sc.,  or  3. 


3  scruples 
8  drams 
12  ounces 


i  dram,  dr.,  or  3 
i  ounce,  oz.,  or  § 
i  pound,  ft> 


LINEAR    MEASURE. 

22.  For  what  is  Linear  Measure  used? 
For  measuring  lines,  distances,  etc. 

23.  What  are  the  denominations  ? 

I  A-iiLTues,  miles,  furlongs,  rods,  yards,  feet,  inches. 
21.  Recite  the  TABU-:. 

12  inches  (in.) 
3  feet 

1 6J  feet,  or 5 £  yards" 

40  rods  * 

8  fur.,  or  3 20  rods  " 


are 
tt 


3  miles 


foot,  ft. 

yard,  yd. 

rod,  perch,  or  pole,  r.  or  p. 
furlong,  fur. 

mile  m. 


league, 


in. 


1  in. 


2  in. 


3  In. 


NOTE.— The  inch  is  commonly  divided  into  halves,  fourth*, 
,  or  truths  ;  pometimrs  into  f/rrff/h*,  culled  linen. 


I'.'O  :    N  ]•      I 

1.  (reorge  may  draw  a  strait  it  lin*-  i  m  :pon 
Markhoanl:  tin-  otli.-rs  on 

2.  V  2  in.  l»i!<_r.     3  in.  loin:.     6  in.  1 

3.  Bow  tang  is  your  Arithmetic?    II..\\  How 
long  i                             H.I\\-  u 

[OW  l»n:r  i-  this  tal>K-  ?     II«»\v  \, 

5.  II.>\v  many  inches  in  3  IVri  ?     In  5  i 

6.  1 1<>\\  man;.  3  yards?     In 

7.  How  many  IV •< -t  in  5  yards  and  t 

1  .w  many  feet  in  24  in.?     In  30  in.?    In  36 
!Iow  manyyards  in  9  IVet  ?    In  15  ft.?    In  2; 

«>TH    >: 

»2.%.  For  what  Is  Cloth  Measure  used? 

r  niraMiriiiLT  dotiis.  laces.  ril»l>o- 
20.  i  Imxv.lividedt 

.  uhich    II 

f'-ir  ih-',  etc, 

•J7.  ;;. 


3  ft,  or  36  in. 

- 

9  in.  " 

4i  in- 


n. 


yard.  //>/. 

half  ;  j  | 

qua;  .     J  yd. 

\  ! 
nth  "       -fg 


;'7,«  Flemi-  Mger 

<-n<nl  is  practically  obsolete. 

1.  How  many  yards  in  S  half;. 

2.  IIow  many  yards  in  16  fourth-!'     In  jS  ! 

3.  I  low  many  yards  in  i ;  •    . 


<  •  O  M  P  0  U  X  1)     T  A  li  I . 


S  Q  r  A  II  E     MEASURE. 
2§.  For  what  is  S<iuare  Measure  used? 

For  measuring  surfaces  ;  as,  land,  flooring,  etc. 

29.  What  are  the  denominations? 

Acres,  square   rods,  square  yards,  square  feet, 
and  square  inches. 

30.  Recite  the  TABLE. 

144  square  in.  (x//.  ///.   are  i   square  foot,       sq.ft. 
()  square  feet  "     i   square  yard,      .sy/.  //</. 

30  £  square  yards,  or  )    "  (  i  square  rod, 
272^  square  t  )       (     perch,  or  pole, 

1 60  sijiuuv  r  "     i   acre.  A. 

640  a  "    i  s([tuire  mile,       *.  ?.'?. 


r. 


1.  A  Sf/Hffi'f-  is  a   rectilinear  figure 
which  has  four  equal  sides,  and  four 
ri'jlit  a 

2.  \stfiiff  re  inch  is  a  square,  each 
Bide  of  which  is  mn'  inch  in  Iciiirth. 

3.  A  sfjn<tr<'  t/<ii'ft  is  a  square,  each 
Bide  of  which  is  one  yard  in  length. 


g  f»q.  ft.  rr  ,  Pq.  yd. 


.  —  i.  Tin  f  any  s(|iuirc 

fiirurc.  also  of   a  bo<jk,  a  table,  a  room, 
'!<•..  are  ri'jlit  <irtf/les. 

2.    Tlie    acre   was    formerly  divided   into  4  roods  ;  but,  in 
,  the  rood  is  no  longer  used  as  a  unit  of  measure. 


1.  Make  a  riirht  jingle  upon  the  blackboard. 

2.  Make  a  square  inch. 

3.  Make  a  square  whose  side  is  3  inches.     6  Indies. 


COM  m  I    N  1»     TA  I,  I 


4.  Make  a  square  foot    A  <<[\\ 

5.  Di\i»k'  ;i  S'|iia:v  \anl  into  ><j 

I  >ivide  a  square  foot  into  stjuuiv  in< •! 

7.  HM\V  many  -<|i; 

8.  How  many  8411  a  r 

CUBIC     MEA> 

31.  For  what  is  Cubic  Measure  used? 

i-  measuring  solids;  as,  timber,  boxes  of  goods, 
the  capacity  of  rooms,  ships,  etc. 

39.  What  are  the  denominations? 

Cords,    cubic    yards,    cubic    feet,   and    cul»i< 

inches. 
33.  Recite  the  TABLE. 

1728  cubic  inches  (cu.  in.)  arc 

27  cul.i'-  " 

128  cubic  feet 


I     (Ml).i('  font, 
I    CO 


x.  A  cube  is  a  regular  solid  bounded  by  fix  equal 


called  ita  faces. 

2.  A  riibir  in  1-Ji  is  a  cube,  each  aide 

of  \vhirh  is  a  square  inch. 

3.  A  cubic  foot  is  a  cube,  each  aide 
of  which  is  a  square  foot. 

4.  A  cubic  utirtl  is  a  rube. each  side 
of  which  is  a  square  yard. 

5.  A   Cortf  of   woo.]  i*  n  pile  8  ft. 
lontj.  4  ft,  wide,  and  4  ft.  hi^rh  ;  for,  8  x 
4x4  =  128. 

6.  A  Card  Foot  =  16  on  ft. .an-: 

loiiir  4  ft.  wi.ir.  ami  }  ft,  high.      8  cord 


(  0  M  P  0  U  X  D     T  A  B  L  E  S  .  l&J 

NOTES. — i.   Timber   is   now  measured   by   cubic   feet   ami 
Inches 

2.  The  old  cubic  ton  of  40  feet  of  round  timber,  or  50  feet  of 
hewn  timber,  has  fallen  into  disuse. 

1.  Draw  a  cubic  inch. 

2.  Draw  a  cube-  whose  sides  arc  2  inches  square. 

3.  Draw  a  cubic  foot. 

4.  How  many  inches  long  and  wide  must  a  block  be 
to  form  a  cubic  foot  ? 

5.  How  many  ilrt  high  is  a  cubic  yard  ? 

6.  How  many  cubic  feet  in  2  cubic  yards? 

DRY     MEASURE. 
Ji  I.  For  what  is  Dry  Measure  used? 

For  measuring  4rr«t*> /rtttf,  salt,  etc. 

JJ5.  What  are  the  denominations  ? 

Chaldrons,  bushels,  pocks,  quarts,  and  pints. 
:*«.   Krrit.-  tin-  TABLE. 

2  pints  (pt.)  arc  i  quart,  qt. 

8  quarts  "  i  peck,  p/c. 

4  pecks,  or  32  qts.,  "  i  bushel,  bu. 

36  bushels  "  i  chaldron,  ch. 


ys  bu.  pk.  yt  pk.        qt.       pt. 

N<»  IK. — The  dry  quart  is  equal  to  i^  liquid  quart  nearly. 

i.   Fn  6  pints,  how  many  quarts?     In  12  pints? 
2     Iii  12  quarts,  how  many  pi •(•!•:. s  ?     In  16  quarts? 


124 


ii"\\  many  quarts  in  3  peck.-;     In  ;  pr« •;-. 
.;.   11. i\v  many  quaris  in  5  , 
5.  In  5  pecks,  how  many  1 
'.  How  many  bushel*  I  IQB?     In  15  p 

7.   How  many  quarts  in  2  1 
&   H"W  many  quarts  in  i  bushel  and  i  p- 
9.    How  many  j.ini  -  ks  ? 


D    MEASURE. 
:tT.  For  what  is  Liquid  Measure  used? 

38.  What  are  tin-  <i<-Mouniuuinna? 

-heads,  barrels,  gallons,  quarts,  pints, 
:::>.   Ut-cite  the  TABLE. 

4  gills  (gi.) 

2  pints  i  «iuart, 

4  quarts  i  L':ill«>n,      gaL 

31 J  gallons  i  borreL       />cr.. 

63  gallons, or  2  bbls.,  "  i  \\<^j;A\ci\(\.  hhd. 


hhd.  bar.  gaL  «;• 


—i.   Licjuid  Measure  is  often  called  Wine  M 
2.  Beer  Measure  is  practically  obeolet.*  in  this  «.in>try 

i.   How  many  LrilN  in  ^  pint-  V     In  6  pii 

j.   Hew  many  pints  in  3  quarts  ?     In  S  quar  - 


M  I'O  L'  >,  1)     T  A  15  L  KS. 


123 


3.  How  many  quarts  in  3  gallons?     Ill  4  gallons? 

4.  How  many  quarts  in  5  gallons  and  2  quarts  ? 

5.  In  1 6  quarts,  how  many  gallons  ? 

6.  In  8  pints,  how  many  quarts?     In  12  pints? 

7.  How  many  quarts  in  13  pints?     In  20  pints? 

8.  In  15  gills,  how  many  pints  ?     In  20  gills  ? 

9.  How  many  quarts  in  6  gallons  and  3  quarts '.' 


CIRCULAR    MEASURE. 

40.  For  what  is  Circular  Measure  used  ? 

For   measuring  c//</lrs,  latitude  and  Invtjitu.dc* 
the  -mot inn  of  the  heavenly  bodies,  ete. 

41.  What  are  the  denominations? 

Signs,  degrees,  minutes,  and  seconds. 

42.  Recite  the  TABLE. 

60  seconds  ")  are  i  minute, 

60  minutes  ••  i  derive, 

30  degr  "  i  sign,                  * 

360  deg:-  "  i  cireumterence,  c  or  dr. 

NOTE. — Signs  are  used  only  in  Astronomy. 

A  Cirrfe  is  a  plane  figure  bound- 
ed by  a  curve  line,  every  part  of 
which  is  equally  distant  from  a 
point  within  called  the  center. 

The  adjoining  figure  is  a  cir- 
ri-. A  D  E  B  F  is  called  the 
circumference ;  A  B,  the  diameter  ; 
C  A.  C  D,  C  E,  etc.,  radii ;  and  A  D,  D  E,  arcs. 


•  i-o  i    N  D    TA  i;  : 


M  I  SC  K  L  1.  A  \ 
12  things  ;uv   i   d 
12  doz.          "     I  gross. 


20    I 


24  sheets  are  i  quire  ]• 

20  ([uires  "    i  ream. 


2      1 

5     humllca  "       i 


3    are  i  1« 

4  leaves      '*  i  <iuarto,  or  4t<x 

8  leaves      "  i  «>,  tavo,  or  8vo. 

.cs      u  i  duodecimo,  or  12  mo. 

18  leaves      "  i  cightern  n 

2^  Icavea      "  i  mo. 

The  tonn- 

her  ol  leaves  into  which  a  sheet  of  paper  is  folded  in  i. 


4  in.  -  i  hand,  for  measuring  the  height  of  horses. 

n  in.   =  i  span. 

18  in.  =  i  rui 

(,  ft    t=  i  fathom,  for  measuring  depths  at  eea. 


32  Ibs.  = 
481bs.  = 


i  bu.  of  oats. 
ur^ 
56  Ibs.  =  i     "    rye,  or  salt. 


58  Ibe.  = 
60  Ibs.  = 
62  Ibs.  =  i  '  beans. 


100  pounds  =  i  quintal  of  dry  fish. 

196  pounds  =  i  barri'l  of  tlour. 

200  pounds  =  i  barrel  of  fish,  beef,  or  pork. 

280  pounds  =  I  barrel  of  salt. 


YA 




••s  NEW  GRADED  SERI 


COMPLETE     IN    THREE     BOOKS. 


L  NEW  MENTAL  ARITHMETIC. 

uta. 

IL  NEW  RUDIMENTS  OF  ARITHMETIC. 
IE.  NEW  PRACTICAL  ARITHMETIC. 

rl.OO. 


complefc 

• 
TK\«  are  usiug  . 


Th^  •  to 


/./)//  ^ 
im  n  vi  i  i 

•  /• 

4  If  /Ml  Mill,.     UK,  II 

h  I    Y     TO    UK  M  1   1  l<   . 


N    B      I-1  particular! 

Lil><  i  ntrodi^t :  °^fl| 

' 


